IMA Journal of Numerical Analysis Short Title: IMA J. Numer. Anal. Publisher: Oxford University Press, Oxford ISSN: 0272-4979; 1464-3642/e Online: https://academic.oup.com/imajna/issue Predecessor: Journal of the Institute of Mathematics and its Applications Comments: Indexed cover-to-cover Documents Indexed: 2,007 Publications (since 1981) all top 5 Latest Issues 43, No. 1 (2023) 42, No. 4 (2022) 42, No. 3 (2022) 42, No. 2 (2022) 42, No. 1 (2022) 41, No. 4 (2021) 41, No. 3 (2021) 41, No. 2 (2021) 41, No. 1 (2021) 40, No. 4 (2020) 40, No. 3 (2020) 40, No. 2 (2020) 40, No. 1 (2020) 39, No. 4 (2019) 39, No. 3 (2019) 39, No. 2 (2019) 39, No. 1 (2019) 38, No. 4 (2018) 38, No. 3 (2018) 38, No. 2 (2018) 38, No. 1 (2018) 37, No. 4 (2017) 37, No. 3 (2017) 37, No. 2 (2017) 37, No. 1 (2017) 36, No. 4 (2016) 36, No. 3 (2016) 36, No. 2 (2016) 36, No. 1 (2016) 35, No. 4 (2015) 35, No. 3 (2015) 35, No. 2 (2015) 35, No. 1 (2015) 34, No. 4 (2014) 34, No. 3 (2014) 34, No. 2 (2014) 34, No. 1 (2014) 33, No. 4 (2013) 33, No. 3 (2013) 33, No. 2 (2013) 33, No. 1 (2013) 32, No. 4 (2012) 32, No. 3 (2012) 32, No. 2 (2012) 32, No. 1 (2012) 31, No. 4 (2011) 31, No. 3 (2011) 31, No. 2 (2011) 31, No. 1 (2011) 30, No. 4 (2010) 30, No. 3 (2010) 30, No. 2 (2010) 30, No. 1 (2010) 29, No. 4 (2009) 29, No. 3 (2009) 29, No. 2 (2009) 29, No. 1 (2009) 28, No. 4 (2008) 28, No. 3 (2008) 28, No. 2 (2008) 28, No. 1 (2008) 27, No. 4 (2007) 27, No. 3 (2007) 27, No. 2 (2007) 27, No. 1 (2007) 26, No. 4 (2006) 26, No. 3 (2006) 26, No. 2 (2006) 26, No. 1 (2006) 25, No. 4 (2005) 25, No. 3 (2005) 25, No. 2 (2005) 25, No. 1 (2005) 24, No. 4 (2004) 24, No. 3 (2004) 24, No. 2 (2004) 24, No. 1 (2004) 23, No. 4 (2003) 23, No. 3 (2003) 23, No. 2 (2003) 23, No. 1 (2003) 22, No. 4 (2002) 22, No. 3 (2002) 22, No. 2 (2002) 22, No. 1 (2002) 21, No. 4 (2001) 21, No. 3 (2001) 21, No. 2 (2001) 21, No. 1 (2001) 20, No. 4 (2000) 20, No. 3 (2000) 20, No. 2 (2000) 20, No. 1 (2000) 19, No. 4 (1999) 19, No. 3 (1999) 19, No. 2 (1999) 19, No. 1 (1999) 18, No. 4 (1998) 18, No. 3 (1998) 18, No. 2 (1998) ...and 46 more Volumes all top 5 Authors 26 Barrett, John William 25 Elliott, Charles M. 24 Iserles, Arieh 16 Süli, Endre E. 14 Sanz-Serna, Jesús María 13 Pani, Amiya Kumar 12 Bernardi, Christine 12 Brunner, Hermann 12 Eymard, Robert 12 Lubich, Christian 12 Powell, Michael James David 12 Sloan, Ian Hugh 12 Stynes, Martin 11 Gatica, Gabriel N. 10 Graham, Ivan G. 10 Herbin, Raphaèle 9 Atkinson, Kendall Eugene 9 Carstensen, Carsten 9 Cockburn, Bernardo 9 Droniou, Jérôme 9 Ern, Alexandre 9 Heuer, Norbert 9 Higham, Nicholas J. 9 Li, Buyang 9 Meddahi, Salim 9 Nicaise, Serge 9 Watson, G. Alistair 9 Yuan, Ya-xiang 8 Burman, Erik 8 Georgoulis, Emmanuil H. 8 Higham, Desmond J. 8 Nørsett, Syvert Paul 8 Nürnberg, Robert 8 Ostermann, Alexander 8 Rodríguez, Rodolfo 8 Sayas, Francisco-Javier 8 Schötzau, Dominik 8 Schwab, Christoph 8 van der Houwen, Pieter J. 7 Akrivis, Georgios D. 7 Banjai, Lehel 7 Fairweather, Graeme 7 Garcke, Harald 7 Hill, Adrian T. 7 Houston, Paul 7 Jin, Bangti 7 Karlsen, Kenneth Hvistendahl 7 Kovács, Balázs 7 Nataraj, Neela 7 Osborne, Michael Robert 7 Praetorius, Dirk 7 Prohl, Andreas 7 Stevenson, Rob P. 6 Ainsworth, Mark 6 Araya, Rodolfo A. 6 Barrenechea, Gabriel R. 6 Bartels, Sören 6 Buhmann, Martin Dietrich 6 Chainais-Hillairet, Claire 6 Chandler-Wilde, Simon N. 6 Dai, Yu-Hong 6 Forsyth, Peter A. 6 Gallouët, Thierry 6 García-Archilla, Bosco 6 Girault, Vivette 6 Grohs, Philipp 6 Guzmán, Johnny 6 Hackbusch, Wolfgang 6 Huybrechs, Daan 6 Maday, Yvon 6 McKee, Sean 6 Meerbergen, Karl 6 Melenk, Jens Markus 6 Moore, Gerald 6 Mora, David 6 Morton, Keith William 6 Phillips, Timothy N. 6 Qiu, Weifeng 6 Sauter, Stefan A. 6 Schöberl, Joachim 6 Sommeijer, Ben P. 6 Tobiska, Lutz 6 Tretyakov, Michael V. 6 Wathen, Andrew John 5 Andreani, Roberto 5 Apel, Thomas 5 Bai, Zhongzhi 5 Baker, Christopher Thomas Hale 5 Blowey, James F. 5 Burrage, Kevin 5 Cooper, Gavin J. 5 Cox, Maurice G. 5 Curtis, Frank E. 5 de Frutos, Javier 5 Deckelnick, Klaus 5 Diening, Lars 5 Dormand, John R. 5 Feng, Xiaobing 5 Griffiths, David F. 5 Guglielmi, Nicola ...and 2,382 more Authors all top 5 Fields 1,854 Numerical analysis (65-XX) 650 Partial differential equations (35-XX) 214 Fluid mechanics (76-XX) 187 Ordinary differential equations (34-XX) 141 Approximations and expansions (41-XX) 109 Integral equations (45-XX) 93 Operations research, mathematical programming (90-XX) 81 Mechanics of deformable solids (74-XX) 63 Probability theory and stochastic processes (60-XX) 61 Calculus of variations and optimal control; optimization (49-XX) 55 Linear and multilinear algebra; matrix theory (15-XX) 50 Optics, electromagnetic theory (78-XX) 42 Dynamical systems and ergodic theory (37-XX) 42 Operator theory (47-XX) 32 Classical thermodynamics, heat transfer (80-XX) 30 Statistical mechanics, structure of matter (82-XX) 25 Functions of a complex variable (30-XX) 24 Harmonic analysis on Euclidean spaces (42-XX) 19 Special functions (33-XX) 19 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 18 Biology and other natural sciences (92-XX) 17 Real functions (26-XX) 17 Quantum theory (81-XX) 15 Potential theory (31-XX) 15 Statistics (62-XX) 14 Global analysis, analysis on manifolds (58-XX) 10 Computer science (68-XX) 9 Integral transforms, operational calculus (44-XX) 9 Differential geometry (53-XX) 8 Mechanics of particles and systems (70-XX) 8 Systems theory; control (93-XX) 8 Information and communication theory, circuits (94-XX) 7 Geophysics (86-XX) 6 Topological groups, Lie groups (22-XX) 5 Functional analysis (46-XX) 5 Astronomy and astrophysics (85-XX) 4 History and biography (01-XX) 4 Combinatorics (05-XX) 4 Number theory (11-XX) 4 Sequences, series, summability (40-XX) 3 Difference and functional equations (39-XX) 2 Group theory and generalizations (20-XX) 2 Abstract harmonic analysis (43-XX) 2 Relativity and gravitational theory (83-XX) 1 Field theory and polynomials (12-XX) 1 Algebraic geometry (14-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 1,736 Publications have been cited 24,607 times in 17,911 Documents Cited by ▼ Year ▼ Two-point step size gradient methods. Zbl 0638.65055Barzilai, Jonathan; Borwein, Jonathan M. 658 1988 Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems. Zbl 1134.65022Bai, Zhongzhi; Golub, Gene H. 280 2007 A descent modified Polak-Ribière-Polyak conjugate gradient method and its global convergence. Zbl 1106.65056Zhang, Li; Zhou, Weijun; Li, Donghui 206 2006 Local error estimates for radial basis function interpolation of scattered data. Zbl 0762.41006Wu, Zong-Min; Schaback, Robert 183 1993 Families of Runge-Kutta-Nyström formulae. Zbl 0624.65059Dormand, J. R.; El-Mikkawy, M. E. A.; Prince, P. J. 179 1987 Descent property and global convergence of the Fletcher-Reeves method with inexact line search. Zbl 0578.65063Al-Baali, M. 178 1985 Computing the nearest correlation matrix – a problem from finance. Zbl 1006.65036Higham, Nicholas J. 162 2002 On the Barzilai and Borwein choice of steplength for the gradient method. Zbl 0778.65045Raydan, Marcos 160 1993 Discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes SUSHI: A scheme using stabilization and hybrid interfaces. Zbl 1202.65144Eymard, R.; Gallouët, T.; Herbin, R. 158 2010 Preconditioned MHSS iteration methods for a class of block two-by-two linear systems with applications to distributed control problems. Zbl 1271.65100Bai, Zhong-Zhi; Benzi, Michele; Chen, Fang; Wang, Zeng-Qi 144 2013 Finite elements on evolving surfaces. Zbl 1120.65102Dziuk, G.; Elliott, C. M. 143 2007 An analysis of the L1 scheme for the subdiffusion equation with nonsmooth data. Zbl 1336.65150Jin, Bangti; Lazarov, Raytcho; Zhou, Zhi 139 2016 \(R\)-linear convergence of the Barzilai and Borwein gradient method. Zbl 1002.65069Dai, Yuhong; Liao, Li-Zhi 136 2002 A new approach to variable selection in least squares problems. Zbl 0962.65036Osborne, M. R.; Presnell, Brett; Turlach, B. A. 125 2000 Numerical methods for \(y''=f(x,y)\) via rational approximations for the cosine. Zbl 0675.65072Coleman, John P. 123 1989 Superconvergence and extrapolation of non-conforming low order finite elements applied to the Poisson equation. Zbl 1068.65122Lin, Qun; Tobiska, Lutz; Zhou, Aihui 121 2005 \(P\)-stability and exponential-fitting methods for \(y''=f(x,y)\). Zbl 0847.65052Coleman, John P.; Ixaru, Liviu Gr. 120 1996 Block preconditioning of real-valued iterative algorithms for complex linear systems. Zbl 1145.65022Benzi, Michele; Bertaccini, Daniele 114 2008 Newton’s method on Riemannian manifolds and a geometric model for the human spine. Zbl 1056.92002Adler, Roy L.; Dedieu, Jean-Pierre; Margulies, Joseph Y.; Martens, Marco; Shub, Mike 109 2002 The numerical computation of connecting orbits in dynamical systems. Zbl 0706.65080Beyn, W.-J. 109 1990 On generalized moving least squares and diffuse derivatives. Zbl 1252.65037Mirzaei, Davoud; Schaback, Robert; Dehghan, Mehdi 108 2012 Conforming and nonconforming virtual element methods for elliptic problems. Zbl 1433.65282Cangiani, Andrea; Manzini, Gianmarco; Sutton, Oliver J. 108 2017 Moment-free numerical integration of highly oscillatory functions. Zbl 1106.65021Olver, Sheehan 100 2006 The numerical stability of barycentric Lagrange interpolation. Zbl 1067.65016Higham, Nicholas J. 98 2004 Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients. Zbl 1120.65004Todor, Radu Alexandru; Schwab, Christoph 98 2007 Numerical solution of the stable, non-negative definite Lyapunov equation. Zbl 0492.65017Hammarling, S. J. 97 1982 Robust numerical methods for contingent claims under jump diffusion processes. Zbl 1134.91405D’Halluin, Y.; Forsyth, P. A.; Vetzal, K. R. 96 2005 A novel fitted finite volume method for the Black-Scholes equation governing option pricing. Zbl 1147.91332Wang, Song 90 2004 Unconditional convergence of the Euler semi-implicit scheme for the three-dimensional incompressible MHD equations. Zbl 1312.76061He, Yinnian 85 2015 Restrictively preconditioned conjugate gradient methods for systems of linear equations. Zbl 1046.65018Bai, Zhongzhi; Li, Guiqing 83 2003 Convergence of Newton’s method and uniqueness of the solution of equations in Banach space. Zbl 0942.65057Wang, Xinghua 78 2000 A discontinuous Galerkin method with weighted averages for advection-diffusion equations with locally small and anisotropic diffusivity. Zbl 1165.65074Ern, Alexandre; Stephansen, Annette F.; Zunino, Paolo 77 2009 Inexact spectral projected gradient methods on convex sets. Zbl 1047.65042Birgin, Ernesto G.; Martínez, José Mario; Raydan, Marcos 77 2003 A virtual element method with arbitrary regularity. Zbl 1293.65146Beirão da Veiga, Lourenco; Manzini, Gianmarco 76 2014 A conforming mixed finite element method for the coupling of fluid flow with porous media flow. Zbl 1157.76025Gatica, Gabriel N.; Meddahi, Salim; Oyarzúa, Ricardo 75 2009 Approximation of the global attractor for the incompressible Navier-Stokes equations. Zbl 0982.76022Hill, Adrian T.; Süli, Endre 75 2000 On convergence rates for the iteratively regularized Gauss-Newton method. Zbl 0881.65050Blaschke, Barbara; Neubauer, Andreas; Scherzer, Otmar 75 1997 Product approximation for non-linear problems in the finite element method. Zbl 0469.65072Christie, I.; Griffiths, D. F.; Mitchell, A. R.; Sanz-Serna, J. M. 74 1981 Realistic eigenvalue bounds for the Galerkin mass matrix. Zbl 0648.65076Wathen, A. J. 74 1987 Finite difference discretization of the cubic Schrödinger equation. Zbl 0762.65070Akrivis, Georgios D. 73 1993 Fitted and unfitted finite-element methods for elliptic equations with smooth interfaces. Zbl 0629.65118Barrett, John W.; Elliott, Charles M. 73 1987 Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion. Zbl 1321.65142Jin, Bangti; Lazarov, Raytcho; Pasciak, Joseph; Zhou, Zhi 71 2015 Block-diagonal preconditioning for spectral stochastic finite-element systems. Zbl 1169.65007Powell, Catherine E.; Elman, Howard C. 70 2009 The stability of the \(\theta\)-methods in the numerical solution of delay differential equations. Zbl 0693.65056Liu, M. Z.; Spijker, M. N. 69 1990 Newton’s method on Riemannian manifolds: Covariant alpha theory. Zbl 1047.65037Dedieu, Jean-Pierre; Priouret, Pierre; Malajovich, Gregorio 68 2003 The cyclic Barzilai-Borwein method for unconstrained optimization. Zbl 1147.65315Dai, Yuhong; Hager, William W.; Schittkowski, Klaus; Zhang, Hongchao 67 2006 Stability of Runge-Kutta methods for trajectory problems. Zbl 0624.65057Cooper, G. J. 66 1987 Stability and convergence of a second-order mixed finite element method for the Cahn-Hilliard equation. Zbl 1433.80005Diegel, Amanda E.; Wang, Cheng; Wise, Steven M. 66 2016 Conservative and nonconservative schemes for the solution of the nonlinear Schrödinger equation. Zbl 0593.65087Sanz-Serna, J. M.; Verwer, J. G. 65 1986 Order conditions for a class of two-step methods for \(y''=f(x,y)\). Zbl 1022.65080Coleman, John P. 65 2003 A class of derivative-free methods for large-scale nonlinear monotone equations. Zbl 1241.65047Li, Qingna; Li, Dong-Hui 65 2011 Clenshaw-Curtis-Filon-type methods for highly oscillatory Bessel transforms and applications. Zbl 1232.65047Xiang, Shuhuang; Cho, Yeol Je; Wang, Haiyong; Brunner, Hermann 64 2011 Upwind difference approximations for degenerate parabolic convection-diffusion equations with a discontinuous coefficient. Zbl 1014.65073Karlsen, K. H.; Risebro, N. H.; Towers, J. D. 63 2002 Toeplitz preconditioners for Toeplitz systems with nonnegative generating functions. Zbl 0737.65022Chan, Raymond H. 63 1991 On the stability of linear multistep methods for Volterra convolution equations. Zbl 0543.65095Lubich, Ch. 63 1983 A modified BFGS algorithm for unconstrained optimization. Zbl 0733.65039Yuan, Yaxiang 63 1991 A cell-centred finite-volume approximation for anisotropic diffusion operators on unstructured meshes in any space dimension. Zbl 1093.65110Eymard, R.; Gallouët, T.; Herbin, R. 61 2006 High-order embedded Runge-Kutta-Nyström formulae. Zbl 0627.65085Dormand, J. R.; El-Mikkawy, M. E. A.; Prince, P. J. 61 1987 A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction-diffusion problems. Zbl 1048.65076Madden, Niall; Stynes, Martin 61 2003 A mixed virtual element method for the pseudostress-velocity formulation of the Stokes problem. Zbl 1433.76071Cáceres, Ernesto; Gatica, Gabriel N. 60 2017 On the numerical quadrature of highly-oscillating integrals. I: Fourier transforms. Zbl 1061.65149Iserles, Arieh 58 2004 A parallel method for time discretization of parabolic equations based on Laplace transformation and quadrature. Zbl 1022.65108Sheen, Dongwoo; Sloan, Ian H.; Thomée, Vidar 58 2003 Stability analysis of Runge-Kutta methods for nonlinear Volterra delay-integro-differential equations. Zbl 1057.65104Zhang, Chengjian; Vandewalle, Stefan 57 2004 Global convergence of a class of trust-region methods for nonconvex minimization in Hilbert space. Zbl 0698.65043Toint, Ph. L. 57 1988 Numerical solvability of Hammerstein integral equations of mixed type. Zbl 0719.65093Ganesh, M.; Joshi, M. C. 56 1991 Well-posedness of \(hp\)-version discontinuous Galerkin methods for fractional diffusion wave equations. Zbl 1310.65128Mustapha, Kassem; Schötzau, Dominik 56 2014 A fourth algebraic order exponentially-fitted Runge-Kutta method for the numerical solution of the Schrödinger equation. Zbl 0990.65079Simos, T. E. 55 2001 A new weak Galerkin finite element method for the Helmholtz equation. Zbl 1323.65116Mu, Lin; Wang, Junping; Ye, Xiu 55 2015 Numerical convergence properties of option pricing PDEs with uncertain volatility. Zbl 1040.91053Pooley, D. M.; Forsyth, P. A.; Vetzal, K. R. 54 2003 A finite difference method for a two-point boundary value problem with a Caputo fractional derivative. Zbl 1339.65097Stynes, Martin; Gracia, José Luis 54 2015 The Galerkin method for integral equations of the first kind with logarithmic kernel: Theory. Zbl 0636.65143Sloan, I. H.; Spence, A. 53 1988 Stability and error estimates for Filon-Clenshaw-Curtis rules for highly oscillatory integrals. Zbl 1231.65060Domínguez, V.; Graham, I. G.; Smyshlyaev, V. P. 53 2011 Error estimates for the approximate solutions of a nonlinear hyperbolic equation given by finite volume schemes. Zbl 0973.65078Eymard, R.; Gallouët, T.; Ghilani, M.; Herbin, R. 52 1998 Solving linear partial differential equations by exponential splitting. Zbl 0676.65116Sheng, Q. 52 1989 Anisotropic interpolation and quasi-Wilson element for narrow quadrilateral meshes. Zbl 1049.65129Chen, Shaochun; Shi, Dongyang; Zhao, Yongcheng 52 2004 The computation of averages from equilibrium and nonequilibrium Langevin molecular dynamics. Zbl 1347.65014Leimkuhler, Benedict; Matthews, Charles; Stoltz, Gabriel 52 2016 Centred TVD schemes for hyperbolic conservation laws. Zbl 0943.65100Toro, E. F.; Billet, S. J. 51 2000 A note on collocation methods for Volterra integro-differential equations with weakly singular kernels. Zbl 0765.65126Tang, Tao 51 1993 \(H^1\)-Galerkin mixed finite element methods for parabolic partial integro-differential equations. Zbl 1008.65101Pani, Amiya K.; Fairweather, Graeme 51 2002 An implicit finite-difference time-stepping method for a sub-diffusion equation, with spatial discretization by finite elements. Zbl 1219.65091Mustapha, Kassem 51 2011 Linearization of matrix polynomials expressed in polynomial bases. Zbl 1158.15022Amiraslani, A.; Corless, R. M.; Lancaster, P. 50 2009 Linearly implicit time discretization of nonlinear parabolic equations. Zbl 0834.65092Lubich, Ch.; Ostermann, A. 50 1995 The calculation of Hopf points by a direct method. Zbl 0521.65070Griewank, A.; Reddien, G. 50 1983 Matrix completion via an alternating direction method. Zbl 1236.65043Chen, Caihua; He, Bingsheng; Yuan, Xiaoming 50 2012 Newton’s method on Riemannian manifolds: Smale’s point estimate theory under the \(\gamma\)-condition. Zbl 1094.65052Li, Chong; Wang, Jinhua 49 2006 A hybrid mixed discontinuous Galerkin finite-element method for convection-diffusion problems. Zbl 1204.65133Egger, Herbert; Schöberl, Joachim 48 2010 Local polynomial reproduction and moving least squares approximation. Zbl 0976.65013Wendland, Holger 48 2001 Convergence properties of the Fletcher-Reeves method. Zbl 0851.65049Dai, Y. H.; Yuan, Y. 48 1996 Stochastic exponential integrators for the finite element discretization of SPDEs for multiplicative and additive noise. Zbl 1272.65010Lord, Gabriel J.; Tambue, Antoine 48 2013 The discrete collocation method for nonlinear integral equations. Zbl 0771.65090Atkinson, K.; Flores, J. 47 1993 Piecewise rational quadratic interpolation to monotonic data. Zbl 0481.65004Gregory, J. A.; Delbourgo, R. 47 1982 Conservative upwind finite-element method for a simplified Keller-Segel system modelling chemotaxis. Zbl 1119.65094Saito, Norikazu 47 2007 Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems I: The scalar case. Zbl 1084.65116Houston, Paul; Robson, Janice; Süli, Endre 47 2005 Pre-asymptotic error analysis of CIP-FEM and FEM for the Helmholtz equation with high wave number. I: Linear version. Zbl 1296.65144Wu, Haijun 47 2014 A second elasticity element using the matrix bubble. Zbl 1232.74101Gopalakrishnan, J.; Guzmán, J. 46 2012 \(\varepsilon\)-uniform schemes with high-order time-accuracy for parabolic singular perturbation problems. Zbl 0942.65095Hemker, P. W.; Shishkin, G. I.; Shishkina, L. P. 45 2000 Approximation of \(1/x\) by exponential sums in \([1, \infty]\). Zbl 1082.65025Braess, Dietrich; Hackbusch, Wolfgang 45 2005 The numerical evaluation of particular solutions for Poisson’s equation. Zbl 0576.65114Atkinson, K. E. 45 1985 Conforming and divergence-free Stokes elements in three dimensions. Zbl 1305.76056Guzmán, Johnny; Neilan, Michael 45 2014 A splitting method for separable convex programming. Zbl 1310.65062He, Bingsheng; Tao, Min; Yuan, Xiaoming 45 2015 Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs. Zbl 07524707Mishra, Siddhartha; Molinaro, Roberto 11 2022 An adaptive BDF2 implicit time-stepping method for the phase field crystal model. Zbl 1493.65168Liao, Hong-Lin; Ji, Bingquan; Zhang, Luming 11 2022 Simulation of McKean-Vlasov SDEs with super-linear growth. Zbl 1481.65020dos Reis, Gonçalo; Engelhardt, Stefan; Smith, Greig 8 2022 The time-fractional Cahn-Hilliard equation: analysis and approximation. Zbl 1497.65158Al-Maskari, Mariam; Karaa, Samir 5 2022 Consistency, convergence and error estimates for a mixed finite element-finite volume scheme to compressible Navier-Stokes equations with general inflow/outflow boundary data. Zbl 07465494Kwon, Young-Sam; Novotný, Antonín 5 2022 Automatic rational approximation and linearization of nonlinear eigenvalue problems. Zbl 07524710Lietaert, Pieter; Meerbergen, Karl; Pérez, Javier; Vandereycken, Bart 4 2022 Divergence-preserving reconstructions on polygons and a really pressure-robust virtual element method for the Stokes problem. Zbl 07465508Frerichs, Derk; Merdon, Christian 4 2022 A posteriori error estimates with boundary correction for a cut finite element method. Zbl 07465500Burman, Erik; He, Cuiyu; Larson, Mats G. 3 2022 Equivalence of local- and global-best approximations, a simple stable local commuting projector, and optimal \(hp\) approximation estimates in \(\boldsymbol{H}(\operatorname{div})\). Zbl 07524708Ern, Alexandre; Gudi, Thirupathi; Smears, Iain; Vohralík, Martin 2 2022 An HDG method for dissimilar meshes. Zbl 1501.65127Solano, Manuel; Terrana, Sébastien; Nguyen, Ngoc-Cuong; Peraire, Jaime 2 2022 Quasi-Newton variable preconditioning for nonlinear nonuniformly monotone elliptic problems posed in Banach spaces. Zbl 1500.65019Borsos, B.; Karátson, J. 2 2022 A strong order 3/4 method for SDEs with discontinuous drift coefficient. Zbl 07465497Müller-Gronbach, Thomas; Yaroslavtseva, Larisa 2 2022 Consistency analysis of the Grünwald-Letnikov approximation in a bounded domain. Zbl 07563208Sousa, Ercília 2 2022 A \(C^1\)-virtual element method of high order for the Brinkman equations in stream function formulation with pressure recovery. Zbl 1500.65097Mora, David; Reales, Carlos; Silgado, Alberth 2 2022 Solving block low-rank linear systems by LU factorization is numerically stable. Zbl 07524706Higham, Nicholas J.; Mary, Theo 1 2022 Total velocity-based finite volume discretization of two-phase Darcy flow in highly heterogeneous media with discontinuous capillary pressure. Zbl 07524714Brenner, K.; Masson, R.; Quenjel, E. H.; Droniou, J. 1 2022 Robust nonconforming virtual element methods for general fourth-order problems with varying coefficients. Zbl 1501.65109Dedner, Andreas; Hodson, Alice 1 2022 The numerical unified transform method for initial-boundary value problems on the half-line. Zbl 07524719Deconinck, Bernard; Trogdon, Thomas; Yang, Xin 1 2022 Plain convergence of adaptive algorithms without exploiting reliability and efficiency. Zbl 1501.65117Gantner, Gregor; Praetorius, Dirk 1 2022 A family of fast fixed point iterations for M/G/1-type Markov chains. Zbl 1498.65056Bini, Dario A.; Latouche, Guy; Meini, Beatrice 1 2022 A spectral-in-time Newton-Krylov method for nonlinear PDE-constrained optimization. Zbl 07524722Güttel, Stefan; Pearson, John W. 1 2022 A posteriori error estimation and space-time adaptivity for a linear stochastic PDE with additive noise. Zbl 07524724Majee, Ananta K.; Prohl, Andreas 1 2022 Semirobust analysis of an H(div)-conforming DG method with semi-implicit time-marching for the evolutionary incompressible Navier-Stokes equations. Zbl 07524725Han, Yongbin; Hou, Yanren 1 2022 Time-dependent acoustic scattering from generalized impedance boundary conditions via boundary elements and convolution quadrature. Zbl 07465490Banjai, Lehel; Lubich, Christian; Nick, Jörg 1 2022 Galerkin approximation of linear problems in Banach and Hilbert spaces. Zbl 07465495Arendt, W.; Chalendar, I.; Eymard, R. 1 2022 Space-time discretization for nonlinear parabolic systems with \(p\)-structure. Zbl 07465498Berselli, Luigi C.; Růžička, Michael 1 2022 Error estimates for fully discrete BDF finite element approximations of the Allen-Cahn equation. Zbl 07465501Akrivis, Georgios; Li, Buyang 1 2022 Wavelet-based approximations of pointwise bound constraints in Lebesgue and Sobolev spaces. Zbl 07465503Dahlke, S.; Surowiec, T. M. 1 2022 A convergent finite element scheme for a fourth-order liquid crystal model. Zbl 07465504Metzger, Stefan 1 2022 Residual-based a posteriori error estimates of mixed methods for a three-field Biot’s consolidation model. Zbl 1493.65157Li, Yuwen; Zikatanov, Ludmil T. 1 2022 Log orthogonal functions: approximation properties and applications. Zbl 1481.65037Chen, Sheng; Shen, Jie 1 2022 Error bounds for overdetermined and underdetermined generalized centred simplex gradients. Zbl 1481.65057Hare, Warren; Jarry-Bolduc, Gabriel; Planiden, Chayne 1 2022 A variational approach to the sum splitting scheme. Zbl 1481.65079Eisenmann, Monika; Hansen, Eskil 1 2022 Stable gradient flow discretizations for simulating bilayer plate bending with isometry and obstacle constraints. Zbl 07563184Bartels, Sören; Palus, Christian 1 2022 An HDG method for the Steklov eigenvalue problem. Zbl 07563185Monk, Peter; Zhang, Yangwen 1 2022 Error analysis for space discretizations of quasilinear wave-type equations. Zbl 1503.65230Hochbruck, Marlis; Maier, Bernhard 1 2022 Uniform error estimates for artificial neural network approximations for heat equations. Zbl 1502.65171Gonon, Lukas; Grohs, Philipp; Jentzen, Arnulf; Kofler, David; Šiška, David 1 2022 Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions. Zbl 1502.65264Grohs, Philipp; Herrmann, Lukas 1 2022 Conforming and nonconforming VEMs for the fourth-order reaction-subdiffusion equation: a unified framework. Zbl 1502.65130Li, Meng; Zhao, Jikun; Huang, Chengming; Chen, Shaochun 1 2022 Galerkin finite element approximation of a stochastic semilinear fractional subdiffusion with fractionally integrated additive noise. Zbl 1502.65127Kang, Wenyan; Egwu, Bernard A.; Yan, Yubin; Pani, Amiya K. 1 2022 An unfitted Eulerian finite element method for the time-dependent Stokes problem on moving domains. Zbl 1502.65147von Wahl, Henry; Richter, Thomas; Lehrenfeld, Christoph 1 2022 Error estimate of a decoupled numerical scheme for the Cahn-Hilliard-Stokes-Darcy system. Zbl 07563204Chen, Wenbin; Wang, Shufen; Zhang, Yichao; Han, Daozhi; Wang, Cheng; Wang, Xiaoming 1 2022 An adaptive edge finite element DtN method for Maxwell’s equations in biperiodic structures. Zbl 07563209Jiang, Xue; Li, Peijun; Lv, Junliang; Wang, Zhoufeng; Wu, Haijun; Zheng, Weiying 1 2022 The dual inverse scaling and squaring algorithm for the matrix logarithm. Zbl 07563210Fasi, Massimiliano; Iannazzo, Bruno 1 2022 An \(L^p\) spaces-based formulation yielding a new fully mixed finite element method for the coupled Darcy and heat equations. Zbl 07607695Gatica, Gabriel N.; Meddahi, Salim; Ruiz-Baier, Ricardo 1 2022 A priori and a posteriori error estimates for a virtual element method for the non-self-adjoint Steklov eigenvalue problem. Zbl 1502.65182Wang, Gang; Meng, Jian; Wang, Ying; Mei, Liquan 1 2022 Stability of Galerkin discretizations of a mixed space-time variational formulation of parabolic evolution equations. Zbl 1461.65242Stevenson, Rob; Westerdiep, Jan 11 2021 Optimal-order error estimates of finite element approximations to variable-order time-fractional diffusion equations without regularity assumptions of the true solutions. Zbl 07528285Zheng, Xiangcheng; Wang, Hong 9 2021 On strong stability of explicit Runge-Kutta methods for nonlinear semibounded operators. Zbl 1464.65075Ranocha, Hendrik 8 2021 Blow-up of error estimates in time-fractional initial-boundary value problems. Zbl 07528268Chen, Hu; Stynes, Martin 8 2021 Nonconforming finite element discretization for semilinear problems with trilinear nonlinearity. Zbl 1460.65145Carstensen, Carsten; Mallik, Gouranga; Nataraj, Neela 7 2021 Energy-preserving methods for nonlinear Schrödinger equations. Zbl 1460.65099Besse, Christophe; Descombes, Stéphane; Dujardin, Guillaume; Lacroix-Violet, Ingrid 7 2021 Adaptive cubic regularization methods with dynamic inexact Hessian information and applications to finite-sum minimization. Zbl 1460.65076Bellavia, Stefania; Gurioli, Gianmarco; Morini, Benedetta 7 2021 Strong error analysis for stochastic gradient descent optimization algorithms. Zbl 1460.65071Jentzen, Arnulf; Kuckuck, Benno; Neufeld, Ariel; von Wurstemberger, Philippe 5 2021 Anderson acceleration for contractive and noncontractive operators. Zbl 07528322Pollock, Sara; Rebholz, Leo G. 5 2021 \(hp\)-FEM for the fractional heat equation. Zbl 1466.65141Markus Melenk, Jens; Rieder, Alexander 4 2021 Convergence in Hölder norms with applications to Monte Carlo methods in infinite dimensions. Zbl 1460.65054Cox, Sonja; Hutzenthaler, Martin; Jentzen, Arnulf; van Neerven, Jan; Welti, Timo 4 2021 Trace finite element methods for surface vector-Laplace equations. Zbl 1466.65192Jankuhn, Thomas; Reusken, Arnold 3 2021 A numerical-analysis-focused comparison of several finite volume schemes for a unipolar degenerate drift-diffusion model. Zbl 1460.65104Cancès, Clément; Chainais-Hillairet, Claire; Fuhrmann, Jürgen; Gaudeul, Benoît 3 2021 Bridging the hybrid high-order and virtual element methods. Zbl 1460.65148Lemaire, Simon 3 2021 Finite element error analysis of wave equations with dynamic boundary conditions: \(L^2\) estimates. Zbl 1460.65120Hipp, David; Kovács, Balázs 3 2021 Trace operators of the bi-Laplacian and applications. Zbl 1501.65116Führer, Thomas; Haberl, Alexander; Heuer, Norbert 3 2021 The Euler-Maruyama scheme for SDEs with irregular drift: convergence rates via reduction to a quadrature problem. Zbl 07528274Neuenkirch, Andreas; Szölgyenyi, Michaela 3 2021 A unified theory for continuous-in-time evolving finite element space approximations to partial differential equations in evolving domains. Zbl 07528292Elliott, C. M.; Ranner, T. 3 2021 An energy-stable parametric finite element method for simulating solid-state dewetting. Zbl 07528298Zhao, Quan; Jiang, Wei; Bao, Weizhu 3 2021 A Banach space mixed formulation for the unsteady Brinkman-Forchheimer equations. Zbl 07528318Caucao, Sergio; Yotov, Ivan 3 2021 A mixed-primal finite element method for the coupling of Brinkman-Darcy flow and nonlinear transport. Zbl 1460.65138Alvarez, Mario; Gatica, Gabriel N.; Ruiz-Baier, Ricardo 2 2021 Multivariate approximation of functions on irregular domains by weighted least-squares methods. Zbl 07528278Migliorati, Giovanni 2 2021 Optimal rate of convergence for two classes of schemes to stochastic differential equations driven by fractional Brownian motions. Zbl 07528288Hong, Jialin; Huang, Chuying; Wang, Xu 2 2021 Space-time discontinuous Galerkin approximation of acoustic waves with point singularities. Zbl 07528299Bansal, Pratyuksh; Moiola, Andrea; Perugia, Ilaria; Schwab, Christoph 2 2021 Domain decomposition preconditioners for high-order discretizations of the heterogeneous Helmholtz equation. Zbl 1501.65151Gong, Shihua; Graham, Ivan G.; Spence, Euan A. 2 2021 Accurately computing the log-sum-exp and softmax functions. Zbl 07528305Blanchard, Pierre; Higham, Desmond J.; Higham, Nicholas J. 2 2021 Analysis of an interior penalty DG method for the quad-curl problem. Zbl 07528327Chen, Gang; Qiu, Weifeng; Xu, Liwei 2 2021 Higher-order discontinuous Galerkin time discretizations for the evolutionary Navier-Stokes equations. Zbl 07528330Ahmed, Naveed; Matthies, Gunar 2 2021 Optimal error estimates and recovery technique of a mixed finite element method for nonlinear thermistor equations. Zbl 07528332Gao, Huadong; Sun, Weiwei; Wu, Chengda 2 2021 Analysis of limited-memory BFGS on a class of nonsmooth convex functions. Zbl 1464.65060Asl, Azam; Overton, Michael L. 1 2021 A log-barrier Newton-CG method for bound constrained optimization with complexity guarantees. Zbl 1464.65067O’Neill, Michael; Wright, Stephen J. 1 2021 Implicit MAC scheme for compressible Navier-Stokes equations: low Mach asymptotic error estimates. Zbl 1460.65108Maltese, David; Novotný, Antonín 1 2021 Contour integrals of analytic functions given on a grid in the complex plane. Zbl 07528264Fornberg, Bengt 1 2021 A convergent FV-FE scheme for the stationary compressible Navier-Stokes equations. Zbl 07528265Perrin, Charlotte; Saleh, Khaled 1 2021 Backward differentiation formula finite difference schemes for diffusion equations with an obstacle term. Zbl 1501.65027Bokanowski, Olivier; Debrabant, Kristian 1 2021 Randomized sketch descent methods for non-separable linearly constrained optimization. Zbl 07528271Necoara, Ion; Takáč, Martin 1 2021 Symmetric pressure stabilization for equal-order finite element approximations to the time-dependent Navier-Stokes equations. Zbl 07528272García-Archilla, Bosco; John, Volker; Novo, Julia 1 2021 Discontinuous Galerkin finite element methods for the Landau-de Gennes minimization problem of liquid crystals. Zbl 1501.65123Maity, Ruma Rani; Majumdar, Apala; Nataraj, Neela 1 2021 A high-frequency boundary element method for scattering by a class of multiple obstacles. Zbl 07528275Gibbs, Andrew; Chandler-Wilde, Simon N.; Langdon, Stephen; Moiola, Andrea 1 2021 Variational integrators for stochastic dissipative Hamiltonian systems. Zbl 07528279Kraus, Michael; Tyranowski, Tomasz M. 1 2021 Hermite interpolation on the unit sphere and limits of Lagrange projectors. Zbl 1497.65021Manh, Phung Van 1 2021 Conforming and nonconforming virtual element methods for a Kirchhoff plate contact problem. Zbl 07528284Wang, Fei; Zhao, Jikun 1 2021 A finite element error analysis for axisymmetric mean curvature flow. Zbl 07528290Barrett, John W.; Deckelnick, Klaus; Nürnberg, Robert 1 2021 Quantitative stability and error estimates for optimal transport plans. Zbl 07528295Li, Wenbo; Nochetto, Ricardo H. 1 2021 Robust a posteriori error estimation for mixed finite element approximation of linear poroelasticity. Zbl 07528297Khan, Arbaz; Silvester, David J. 1 2021 Numerical analysis for nematic electrolytes. Zbl 07528302Baňas, Ľubomír; Lasarzik, Robert; Prohl, Andreas 1 2021 Post-processing of the plane-wave approximation of Schrödinger equations. II: Kohn-Sham models. Zbl 07528310Dusson, Geneviève 1 2021 Optimal finite element error estimates for an optimal control problem governed by the wave equation with controls of bounded variation. Zbl 07528316Engel, Sebastian; Vexler, Boris; Trautmann, Philip 1 2021 A second-order discretization for degenerate systems of stochastic differential equations. Zbl 07528320Iguchi, Yuga; Yamada, Toshihiro 1 2021 Strong approximation of monotone stochastic partial differential equations driven by white noise. Zbl 1464.65148Liu, Zhihui; Qiao, Zhonghua 14 2020 Fully discrete finite element approximation of unsteady flows of implicitly constituted incompressible fluids. Zbl 1464.65131Süli, Endre; Tscherpel, Tabea 12 2020 Strong convergence rates for an explicit numerical approximation method for stochastic evolution equations with non-globally Lipschitz continuous nonlinearities. Zbl 1466.65161Jentzen, Arnulf; Pušnik, Primož 12 2020 A priori and a posteriori error estimates for a virtual element spectral analysis for the elasticity equations. Zbl 1466.65197Mora, David; Rivera, Gonzalo 10 2020 Pointwise-in-time error estimates for an optimal control problem with subdiffusion constraint. Zbl 1464.65065Jin, Bangti; Li, Buyang; Zhou, Zhi 10 2020 ...and 1632 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 16,653 Authors 203 Simos, Theodore E. 103 Dehghan Takht Fooladi, Mehdi 81 Shi, Dongyang 74 Gatica, Gabriel N. 66 He, Yinnian 62 Argyros, Ioannis Konstantinos 59 Zhang, Guofeng 58 Huang, Yunqing 53 Xiang, Shuhuang 53 Xu, Da 52 Li, Jichun 51 Carstensen, Carsten 48 Praetorius, Dirk 48 Reichel, Lothar 47 Chen, Yanping 47 Ern, Alexandre 46 Huang, Chengming 46 Wu, Xinyuan 43 Sayas, Francisco-Javier 42 Stynes, Martin 42 Wang, Song 41 Di Pietro, Daniele Antonio 41 Iserles, Arieh 41 Ma, Changfeng 40 Burman, Erik 40 Li, Buyang 40 Schwab, Christoph 40 Zhang, Zhimin 39 Dai, Yu-Hong 39 Droniou, Jérôme 39 Ruiz-Baier, Ricardo 38 Vohralík, Martin 37 Zhang, Chengjian 36 Eymard, Robert 36 Mora, David 36 Pani, Amiya Kumar 34 Antonietti, Paola Francesca 34 Babaie-Kafaki, Saman 34 Manzini, Gianmarco 33 Beirão da Veiga, Lourenço 33 Heuer, Norbert 33 Zhang, Shangyou 32 Barrett, John William 32 Chung, Tsz Shun Eric 32 He, Xiaoming 32 Liang, Zhaozheng 32 Melenk, Jens Markus 32 Oyarzúa, Ricardo 32 Wang, Wansheng 31 Bai, Zhongzhi 31 Benner, Peter 31 Cockburn, Bernardo 31 Feng, Xinlong 31 Mao, Shipeng 31 Martínez, José Mario 31 Olshanskii, Maxim A. 30 Alolyan, Ibraheem 29 Chen, Shaochun 29 Jentzen, Arnulf 29 Nicaise, Serge 29 Sanz-Serna, Jesús María 29 Wang, Cheng 28 Brunner, Hermann 28 Li, Donghui 28 Nelakanti, Gnaneshwar 28 Toint, Philippe L. 27 Elliott, Charles M. 27 Li, Chong 27 Lin, Yanping 27 Serra-Capizzano, Stefano 27 Yuan, Gonglin 26 Fang, Yonglei 26 Forsyth, Peter A. 26 Führer, Thomas 26 Georgoulis, Emmanuil H. 26 Gracia, José Luis 26 Guo, Ben-Yu 26 Hansbo, Peter 26 Herbin, Raphaèle 26 Karlsen, Kenneth Hvistendahl 26 Larson, Mats G. 26 Liu, Hongwei 26 Paternoster, Beatrice 26 Verani, Marco 26 Wu, Yujiang 25 Abbaszadeh, Mostafa 25 Cao, Yang 25 Clavero, Carmelo 25 Ganesh, Mahadevan 25 George, Santhosh 25 Han, Weimin 25 Harbrecht, Helmut 25 Jin, Bangti 25 Kadalbajoo, Mohan K. 25 Lubich, Christian 25 Nochetto, Ricardo Horacio 25 Otárola, Enrique 25 Wei, Zengxin 25 Wu, Zongmin 24 Ford, Neville J. ...and 16,553 more Authors all top 5 Cited in 719 Journals 1,449 Journal of Computational and Applied Mathematics 914 Applied Mathematics and Computation 764 Computers & Mathematics with Applications 763 Applied Numerical Mathematics 636 Journal of Computational Physics 605 Journal of Scientific Computing 526 Numerische Mathematik 509 Computer Methods in Applied Mechanics and Engineering 509 Numerical Algorithms 464 Mathematics of Computation 353 International Journal of Computer Mathematics 350 SIAM Journal on Scientific Computing 339 SIAM Journal on Numerical Analysis 277 BIT 242 Advances in Computational Mathematics 234 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 201 Linear Algebra and its Applications 179 Calcolo 179 Numerical Methods for Partial Differential Equations 176 Computational Optimization and Applications 171 Computational and Applied Mathematics 160 Journal of Mathematical Analysis and Applications 156 Engineering Analysis with Boundary Elements 151 Applied Mathematics Letters 148 Journal of Mathematical Chemistry 140 Journal of Optimization Theory and Applications 120 Mathematics and Computers in Simulation 117 Numerical Functional Analysis and Optimization 117 Optimization Methods & Software 108 M\(^3\)AS. 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