SIAM Journal on Numerical Analysis Short Title: SIAM J. Numer. Anal. Publisher: Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA ISSN: 0036-1429; 1095-7170/e Online: http://epubs.siam.org/loi/sjnaam Predecessor: Journal of the Society for Industrial and Applied Mathematics. Series B, Numerical Analysis Comments: Journal; Indexed cover-to-cover Documents Indexed: 6,059 Publications (since 1966) References Indexed: 1,219 Publications with 43,736 References. all top 5 Latest Issues 62, No. 5 (2024) 62, No. 4 (2024) 62, No. 3 (2024) 62, No. 2 (2024) 62, No. 1 (2024) 61, No. 6 (2023) 61, No. 5 (2023) 61, No. 4 (2023) 61, No. 3 (2023) 61, No. 2 (2023) 61, No. 1 (2023) 60, No. 6 (2022) 60, No. 5 (2022) 60, No. 4 (2022) 60, No. 3 (2022) 60, No. 2 (2022) 60, No. 1 (2022) 59, No. 6 (2021) 59, No. 5 (2021) 59, No. 4 (2021) 59, No. 3 (2021) 59, No. 2 (2021) 59, No. 1 (2021) 58, No. 6 (2020) 58, No. 5 (2020) 58, No. 4 (2020) 58, No. 3 (2020) 58, No. 2 (2020) 58, No. 1 (2020) 57, No. 6 (2019) 57, No. 5 (2019) 57, No. 4 (2019) 57, No. 3 (2019) 57, No. 2 (2019) 57, No. 1 (2019) 56, No. 6 (2018) 56, No. 5 (2018) 56, No. 4 (2018) 56, No. 3 (2018) 56, No. 2 (2018) 56, No. 1 (2018) 55, No. 6 (2017) 55, No. 5 (2017) 55, No. 4 (2017) 55, No. 3 (2017) 55, No. 2 (2017) 55, No. 1 (2017) 54, No. 6 (2016) 54, No. 5 (2016) 54, No. 4 (2016) 54, No. 3 (2016) 54, No. 2 (2016) 54, No. 1 (2016) 53, No. 6 (2015) 53, No. 5 (2015) 53, No. 4 (2015) 53, No. 3 (2015) 53, No. 2 (2015) 53, No. 1 (2015) 52, No. 6 (2014) 52, No. 5 (2014) 52, No. 4 (2014) 52, No. 3 (2014) 52, No. 2 (2014) 52, No. 1 (2014) 51, No. 6 (2013) 51, No. 5 (2013) 51, No. 4 (2013) 51, No. 3 (2013) 51, No. 2 (2013) 51, No. 1 (2013) 50, No. 6 (2012) 50, No. 5 (2012) 50, No. 4 (2012) 50, No. 3 (2012) 50, No. 2 (2012) 50, No. 1 (2012) 49, No. 6 (2011) 49, No. 5 (2011) 49, No. 4 (2011) 49, No. 3 (2011) 49, No. 2 (2011) 49, No. 1 (2011) 48, No. 6 (2010) 48, No. 5 (2010) 48, No. 4 (2010) 48, No. 3 (2010) 48, No. 2 (2010) 48, No. 1 (2010) 47, No. 6 (2010) 47, No. 5 (2009) 47, No. 4 (2009) 47, No. 3 (2009) 47, No. 2 (2009) 47, No. 1 (2009) 46, No. 6 (2008) 46, No. 5 (2008) 46, No. 4 (2008) 46, No. 3 (2008) 46, No. 2 (2008) ...and 151 more Volumes all top 5 Authors 41 Carstensen, Carsten 37 Manteuffel, Thomas A. 37 Wheeler, Mary Fanett 36 Babuška, Ivo 35 Du, Qiang 31 Cockburn, Bernardo 31 Nochetto, Ricardo Horacio 31 Shu, Chi-Wang 30 Shen, Jie 29 Cai, Zhiqiang 29 McCormick, Steve Fahrney 26 Sloan, Ian Hugh 26 Sun, Weiwei 25 Li, Buyang 25 Schwab, Christoph 24 Gunzburger, Max D. 24 Süli, Endre E. 23 Ainsworth, Mark 22 Ewing, Richard Edward 21 Burman, Erik 20 Bartels, Sören 20 Guermond, Jean-Luc 20 Rheinboldt, Werner C. 20 Widlund, Olof B. 19 Osher, Stanley Joel 19 Starke, Gerhard 19 Tadmor, Eitan 18 Wohlmuth, Barbara I. 18 Zhang, Zhimin 17 Bank, Randolph E. 17 Ern, Alexandre 17 Feng, Xiaobing 17 Gopalakrishnan, Jay 17 Kelley, Carl T. 17 Layton, William J. 17 Lubich, Christian 17 Parter, Seymour V. 17 Russell, Robert D. 17 Schumaker, Larry L. 17 Wang, Junping 16 Beirão da Veiga, Lourenço 16 Durán, Ricardo G. 16 Fairweather, Graeme 16 Lazarov, Raytcho D. 16 Maday, Yvon 16 Quarteroni, Alfio M. 16 Walkington, Noel J. 15 Arbogast, Todd 15 Bernardi, Christine 15 Dahmen, Wolfgang A. 15 Prohl, Andreas 15 Tang, Tao 15 Thomée, Vidar 14 Atkinson, Kendall Eugene 14 Bao, Weizhu 14 Barrett, John William 14 Brunner, Hermann 14 Dawson, Clint N. 14 Demkowicz, Leszek 14 Gottlieb, David I. 14 Kreiss, Heinz-Otto 14 Lin, Yanping 14 Liu, Steve Wenbin 14 Makridakis, Charalambos G. 14 Reusken, Arnold 14 Stroud, Arthur H. 14 Wang, Hong 14 Wu, Haijun 14 Xu, Jinchao 14 Yotov, Ivan 13 Bialecki, Bernard 13 Burrage, Kevin 13 Conn, Andrew Roger 13 Demlow, Alan 13 Dupont, Todd F. 13 Gander, Martin Jakob 13 George, Alan 13 Graham, Ivan G. 13 Heuer, Norbert 13 Johnson, Claes G. L. 13 Nicolaides, Roy A. 13 Ostermann, Alexander 13 Schötzau, Dominik 13 Stuart, Andrew M. 13 Trefethen, Lloyd Nicholas 12 Ascher, Uri M. 12 Bochev, Pavel B. 12 Brenner, Susanne Cecelia 12 Chan, Tony Fan-Cheong 12 Falk, Richard S. 12 Jin, Shi 12 Joly, Patrick 12 Luskin, Mitchell 12 Ma, Heping 12 Novo, Julia 12 Pareschi, Lorenzo 12 Petzold, Linda Ruth 12 Sauter, Stefan 12 Xu, Xuejun 11 Bramble, James H. ...and 5,354 more Authors all top 5 Fields 5,464 Numerical analysis (65-XX) 2,415 Partial differential equations (35-XX) 785 Fluid mechanics (76-XX) 472 Approximations and expansions (41-XX) 450 Ordinary differential equations (34-XX) 271 Mechanics of deformable solids (74-XX) 265 Calculus of variations and optimal control; optimization (49-XX) 252 Integral equations (45-XX) 221 Probability theory and stochastic processes (60-XX) 181 Optics, electromagnetic theory (78-XX) 178 Operations research, mathematical programming (90-XX) 163 Operator theory (47-XX) 149 Statistical mechanics, structure of matter (82-XX) 135 Linear and multilinear algebra; matrix theory (15-XX) 111 Dynamical systems and ergodic theory (37-XX) 100 Computer science (68-XX) 78 Harmonic analysis on Euclidean spaces (42-XX) 68 Functional analysis (46-XX) 64 Biology and other natural sciences (92-XX) 59 Systems theory; control (93-XX) 57 Functions of a complex variable (30-XX) 54 Real functions (26-XX) 53 Special functions (33-XX) 53 Statistics (62-XX) 45 Potential theory (31-XX) 44 Quantum theory (81-XX) 43 Global analysis, analysis on manifolds (58-XX) 43 Geophysics (86-XX) 43 Information and communication theory, circuits (94-XX) 40 Classical thermodynamics, heat transfer (80-XX) 38 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 34 Mechanics of particles and systems (70-XX) 30 Integral transforms, operational calculus (44-XX) 23 Number theory (11-XX) 23 Differential geometry (53-XX) 16 Difference and functional equations (39-XX) 13 Combinatorics (05-XX) 13 Sequences, series, summability (40-XX) 10 Astronomy and astrophysics (85-XX) 9 Field theory and polynomials (12-XX) 9 Algebraic geometry (14-XX) 5 Commutative algebra (13-XX) 5 Convex and discrete geometry (52-XX) 5 Relativity and gravitational theory (83-XX) 4 Algebraic topology (55-XX) 3 Group theory and generalizations (20-XX) 3 Topological groups, Lie groups (22-XX) 3 Measure and integration (28-XX) 3 Manifolds and cell complexes (57-XX) 2 History and biography (01-XX) 2 Geometry (51-XX) 2 Mathematics education (97-XX) 1 General and overarching topics; collections (00-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Associative rings and algebras (16-XX) 1 Several complex variables and analytic spaces (32-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 5,708 Publications have been cited 163,537 times in 78,351 Documents Cited by ▼ Year ▼ Unified analysis of discontinuous Galerkin methods for elliptic problems. Zbl 1008.65080 Arnold, Douglas N.; Brezzi, Franco; Cockburn, Bernardo; Marini, L. Donatella 1,490 2002 The local discontinuous Galerkin method for time-dependent convection-diffusion systems. Zbl 0927.65118 Cockburn, Bernardo; Shu, Chi-Wang 1,149 1998 On the construction and comparison of difference schemes. Zbl 0184.38503 Strang, Gilbert 1,017 1968 Splitting algorithms for the sum of two nonlinear operators. Zbl 0426.65050 Lions, Pierre-Louis; Mercier, B. 864 1979 An interior penalty finite element method with discontinuous elements. Zbl 0482.65060 Arnold, Douglas N. 766 1982 High resolution schemes using flux limiters for hyperbolic conservation laws. Zbl 0565.65048 Sweby, P. K. 718 1984 The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. Zbl 0811.65083 LeVeque, Randall J.; Li, Zhilin 713 1994 A convergent adaptive algorithm for Poisson’s equation. Zbl 0854.65090 Dörfler, Willy 652 1996 Unified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems. Zbl 1205.65312 Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Lazarov, Raytcho 647 2009 Inexact Newton methods. Zbl 0478.65030 Dembo, Ron S.; Eisenstat, Stanley C.; Steihaug, Trond 568 1982 A nonmonotone line search technique for Newton’s method. Zbl 0616.65067 Grippo, L.; Lampariello, F.; Lucidi, S. 559 1986 Error analysis of a finite difference method on graded meshes for a time-fractional diffusion equation. Zbl 1362.65089 Stynes, Martin; O’Riordan, Eugene; Gracia, José Luis 540 2017 Solution of sparse indefinite systems of linear equations. Zbl 0319.65025 Paige, C. C.; Saunders, M. A. 539 1975 Finite-element approximation of the nonstationary Navier-Stokes problem. IV: Error analysis for second-order time discretization. Zbl 0694.76014 Heywood, John G.; Rannacher, Rolf 527 1990 Error estimates for adaptive finite element computations. Zbl 0398.65069 Babuška, Ivo; Rheinboldt, W. C. 527 1978 Finite element approximation of the nonstationary Navier-Stokes problem. I. Regularity of solutions and second-order error estimates for spatial discretization. Zbl 0487.76035 Heywood, John G.; Rannacher, Rolf 486 1982 Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures. Zbl 0492.65051 Douglas, Jim jun.; Russell, Thomas F. 471 1982 Implicit-explicit methods for time-dependent partial differential equations. Zbl 0841.65081 Ascher, Uri M.; Ruuth, Steven J.; Wetton, Brian T. R. 470 1995 Two-grid discretization techniques for linear and nonlinear PDEs. Zbl 0860.65119 Xu, Jinchao 459 1996 A stochastic collocation method for elliptic partial differential equations with random input data. Zbl 1151.65008 Babuška, Ivo; Nobile, Fabio; Tempone, Raúl 452 2007 A space-time spectral method for the time fractional diffusion equation. Zbl 1193.35243 Li, Xianjuan; Xu, Chuanju 451 2009 Galerkin finite element approximations of stochastic elliptic partial differential equations. Zbl 1080.65003 Babuska, Ivo; Tempone, Raúl; Zouraris, Georgios E. 411 2004 A sparse grid stochastic collocation method for partial differential equations with random input data. Zbl 1176.65137 Nobile, F.; Tempone, R.; Webster, C. G. 396 2008 An elliptic collocation-finite element method with interior penalties. Zbl 0384.65058 Wheeler, Mary Fanett 390 1978 Strong convergence of Euler-type methods for nonlinear stochastic differential equations. Zbl 1026.65003 Higham, Desmond J.; Mao, Xuerong; Stuart, Andrew M. 362 2002 Uniformly high-order accurate nonoscillatory schemes. I. Zbl 0627.65102 Harten, Ami; Osher, Stanley 361 1987 The rotation of eigenvectors by a perturbation. III. Zbl 0198.47201 Davis, Chandler; Kahan, W. M. 351 1970 Numerical methods for the variable-order fractional advection-diffusion equation with a nonlinear source term. Zbl 1204.26013 Zhuang, P.; Liu, Fawang; Anh, V.; Turner, I. 340 2009 Finite element method for the space and time fractional Fokker-Planck equation. Zbl 1416.65344 Deng, Weihua 334 2009 Coupling fluid flow with porous media flow. Zbl 1037.76014 Layton, William J.; Schieweck, Friedhelm; Yotov, Ivan 332 2003 An explicit finite difference method and a new von Neumann-type stability analysis for fractional diffusion equations. Zbl 1119.65379 Yuste, S. B.; Acedo, L. 332 2005 High-resolution conservative algorithms for advection in incompressible flow. Zbl 0852.76057 LeVeque, Randall J. 324 1996 Virtual elements for linear elasticity problems. Zbl 1268.74010 Beirao da Veiga, L.; Brezzi, F.; Marini, L. D. 324 2013 On the \(O(1/n)\) convergence rate of the Douglas-Rachford alternating direction method. Zbl 1245.90084 He, Bingsheng; Yuan, Xiaoming 316 2012 A well-balanced scheme for the numerical processing of source terms in hyperbolic equations. Zbl 0876.65064 Greenberg, James M.; Le Roux, Alain-Yves 312 1996 Stability theory for systems of inequalities. II: Differentiable nonlinear systems. Zbl 0347.90050 Robinson, Stephen M. 301 1976 High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations. Zbl 0736.65066 Osher, Stanley; Shu, Chi-Wang 297 1991 A new class of optimal high-order strong-stability-preserving time discretization methods. Zbl 1020.65064 Spiteri, Raymond J.; Ruuth, Steven J. 296 2002 An energy-stable and convergent finite-difference scheme for the phase field crystal equation. Zbl 1201.35027 Wise, S. M.; Wang, Cheng; Lowengrub, J. S. 296 2009 Variational iterative methods for nonsymmetric systems of linear equations. Zbl 0524.65019 Eisenstat, Stanley C.; Elman, Howard C.; Schultz, Martin H. 294 1983 On Krylov subspace approximations to the matrix exponential operator. Zbl 0888.65032 Hochbruck, Marlis; Lubich, Christian 293 1997 A priori \(L_2\) error estimates for Galerkin approximations to parabolic partial differential equations. Zbl 0232.35060 Wheeler, Mary Fanett 291 1972 Poincaré–Friedrichs inequalities for piecewise \(H^{1}\) functions. Zbl 1045.65100 Brenner, Susanne C. 282 2003 Sharp error estimate of the nonuniform L1 formula for linear reaction-subdiffusion equations. Zbl 1447.65026 Liao, Hong-lin; Li, Dongfang; Zhang, Jiwei 276 2018 On Godunov-type methods for gas dynamics. Zbl 0642.76088 Einfeldt, Bernd 275 1988 Second-order convex splitting schemes for gradient flows with Ehrlich-Schwoebel type energy: Application to thin film epitaxy. Zbl 1247.65088 Shen, Jie; Wang, Cheng; Wang, Xiaoming; Wise, Steven M. 274 2012 An algorithm for generalized matrix eigenvalue problems. Zbl 0253.65019 Moler, C. B.; Stewart, G. W. 273 1973 Diagonally implicit Runge-Kutta methods for stiff O.D.E.’s. Zbl 0374.65038 Alexander, Roger 273 1977 Quasi-optimal convergence rate for an adaptive finite element method. Zbl 1176.65122 Cascon, J. Manuel; Kreuzer, Christian; Nochetto, Ricardo H.; Siebert, Kunibert G. 272 2008 Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics. Zbl 1075.65118 Kunisch, K.; Volkwein, S. 270 2002 Inexact and preconditioned Uzawa algorithms for saddle point problems. Zbl 0815.65041 Elman, Howard C.; Golub, Gene H. 270 1994 Stabilization of low-order mixed finite elements for the Stokes equations. Zbl 1145.76015 Bochev, Pavel B.; Dohrmann, Clark R.; Gunzburger, Max D. 266 2006 An a priori error analysis of the local discontinuous Galerkin method for elliptic problems. Zbl 0987.65111 Castillo, Paul; Cockburn, Bernardo; Perugia, Ilaria; Schötzau, Dominik 265 2000 Image selective smoothing and edge detection by nonlinear diffusion. Zbl 0746.65091 Catté, Francine; Lions, Pierre-Louis; Morel, Jean-Michel; Coll, Tomeu 264 1992 Error estimate procedure in the finite element method and applications. Zbl 0582.65078 Ladeveze, P.; Leguillon, D. 263 1983 Nested dissection of a regular finite element mesh. Zbl 0259.65087 George, Alan 254 1973 Some error estimates for the box method. Zbl 0634.65105 Bank, Randolph E.; Rose, Donald J. 249 1987 Discontinuous \(hp\)-finite element methods for advection-diffusion-reaction problems. Zbl 1015.65067 Houston, Paul; Schwab, Christoph; Süli, Endre 248 2002 On direct methods for solving Poisson’s equations. Zbl 0217.52902 Buzbee, B. L.; Golub, G. H.; Nielson, C. W. 245 1970 A Crank-Nicolson ADI spectral method for a two-dimensional Riesz space fractional nonlinear reaction-diffusion equation. Zbl 1382.65349 Zeng, Fanhai; Liu, Fawang; Li, Changpin; Burrage, Kevin; Turner, Ian; Anh, V. 245 2014 New solution and analytical techniques of the implicit numerical method for the anomalous subdiffusion equation. Zbl 1173.26006 Zhuang, P.; Liu, Fawang; Anh, V.; Turner, I. 243 2008 Special finite element methods for a class of second order elliptic problems with rough coefficients. Zbl 0807.65114 Babuška, Ivo; Caloz, Gabriel; Osborn, John E. 242 1994 Numerical methods for nonconservative hyperbolic systems: A theoretical framework. Zbl 1130.65089 Parés, Carlos 240 2006 Analysis of the inexact Uzawa algorithm for saddle point problems. Zbl 0873.65031 Bramble, James H.; Pasciak, Joseph E.; Vassilev, Apostol T. 236 1997 Adaptive finite element methods for parabolic problems. I: A linear model problem. Zbl 0732.65093 Eriksson, Kenneth; Johnson, Claes 232 1991 A mortar finite element method using dual spaces for the Lagrange multiplier. Zbl 0974.65105 Wohlmuth, Barbara I. 232 2000 Analysis of some Krylov subspace approximations to the matrix exponential operator. Zbl 0749.65030 Saad, Y. 231 1992 Stability analysis of large time-stepping methods for epitaxial growth models. Zbl 1127.65069 Xu, Chuanju; Tang, Tao 228 2006 Monotone piecewise cubic interpolation. Zbl 0423.65011 Fritsch, F. N.; Carlson, R. E. 227 1980 Explicit exponential Runge-Kutta methods for semilinear parabolic problems. Zbl 1093.65052 Hochbruck, Marlis; Ostermann, Alexander 225 2005 Data oscillation and convergence of adaptive FEM. Zbl 0970.65113 Morin, Pedro; Nochetto, Ricardo H.; Siebert, Kunibert G. 224 2000 A posteriori error estimates for a discontinuous Galerkin approximation of second-order elliptic problems. Zbl 1058.65120 Karakashian, Ohannes A.; Pascal, Frederic 223 2003 Collocation at Gaussian points. Zbl 0232.65065 de Boor, Carl; Swartz, Blair 221 1973 The conjugate gradient method and trust regions in large scale optimization. Zbl 0518.65042 Steihaug, Trond 220 1983 An anisotropic sparse grid stochastic collocation method for partial differential equations with random input data. Zbl 1176.65007 Nobile, F.; Tempone, R.; Webster, C. G. 218 2008 A local discontinuous Galerkin method for KdV type equations. Zbl 1021.65050 Yan, Jue; Shu, Chi-Wang 215 2002 Iterative solution of implicit approximations of multidimensional partial differential equations. Zbl 0197.13304 Stone, H. L. 215 1968 The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate. Zbl 0258.65045 Golub, G. H.; Pereyra, V. 212 1973 A priori error estimates for finite element methods based on discontinuous approximation spaces for elliptic problems. Zbl 1010.65045 Rivière, Béatrice; Wheeler, Mary F.; Girault, Vivette 210 2001 An analysis of the total least squares problem. Zbl 0468.65011 Golub, Gene H.; Van Loan, Charles F. 209 1980 An energy stable and convergent finite-difference scheme for the modified phase field crystal equation. Zbl 1230.82005 Wang, C.; Wise, S. M. 209 2011 Stability analysis of numerical schemes for stochastic differential equations. Zbl 0869.60052 Saito, Yoshihiro; Mitsui, Taketomo 207 1996 Mean-square and asymptotic stability of the stochastic theta method. Zbl 0982.60051 Higham, Desmond J. 205 2000 Mixed finite elements for elliptic problems with tensor coefficients as cell-centered finite differences. Zbl 0880.65084 Arbogast, Todd; Wheeler, Mary F.; Yotov, Ivan 204 1997 Optimized Schwarz methods. Zbl 1117.65165 Gander, Martin J. 204 2006 Error estimates for a semidiscrete finite element method for fractional order parabolic equations. Zbl 1268.65126 Jin, Bangti; Lazarov, Raytcho; Zhou, Zhi 204 2013 On the accuracy of the finite volume element method based on piecewise linear polynomials. Zbl 1036.65084 Ewing, Richard E.; Lin, Tao; Lin, Yanping 203 2002 A discrete Grönwall inequality with applications to numerical schemes for subdiffusion problems. Zbl 1414.65008 Liao, Hong-lin; McLean, William; Zhang, Jiwei 202 2019 On the angle condition in the finite element method. Zbl 0324.65046 Babuška, Ivo; Aziz, A. K. 201 1976 Application of an ultra weak variational formulation of elliptic PDEs to the two-dimensional Helmholtz problem. Zbl 0955.65081 Cessenat, Olivier; Despres, Bruno 200 1998 Explicit Runge-Kutta (-Nyström) methods with reduced phase errors for computing oscillating solutions. Zbl 0624.65058 Van der Houwen, P. J.; Sommeijer, B. P. 200 1987 Convergence and error analysis for the scalar auxiliary variable (SAV) schemes to gradient flows. Zbl 1403.65047 Shen, Jie; Xu, Jie 196 2018 Two-level method based on finite element and Crank-Nicolson extrapolation for the time-dependent Navier-Stokes equations. Zbl 1130.76365 He, Yinnian 195 2003 Finite element solution of the Helmholtz equation with high wave number. II: The \(h-p\) version of the FEM. Zbl 0884.65104 Ihlenburg, Frank; Babuška, Ivo 195 1997 A family of fourth-order methods for nonlinear equations. Zbl 0266.65040 King, Richard F. 195 1973 A two-grid method of a mixed Stokes-Darcy model for coupling fluid flow with porous media flow. Zbl 1146.76031 Mu, Mo; Xu, Jinchao 195 2007 A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds. Zbl 0724.65067 Conn, Andrew R.; Gould, Nicholas I. M.; Toint, Philippe L. 193 1991 Fundamental solutions method for elliptic boundary value problems. Zbl 0579.65121 Bogomolny, Alexander 192 1985 Comparing numerical methods for ordinary differential equations. Zbl 0221.65115 Hull, T. E.; Enright, W. H.; Fellen, B. M.; Sedgwick, A. E. 190 1972 Convergence of the mimetic finite difference method for diffusion problems on polyhedral meshes. Zbl 1108.65102 Brezzi, Franco; Lipnikov, Konstantin; Shashkov, Mikhail 189 2005 Optimal error bounds on the exponential wave integrator for the nonlinear Schrödinger equation with low regularity potential and nonlinearity. Zbl 1531.35290 Bao, Weizhu; Wang, Chushan 5 2024 On uncertainty quantification of eigenvalues and eigenspaces with higher multiplicity. Zbl 07805447 Dölz, Jürgen; Ebert, David 3 2024 Numerical methods and analysis of computing quasiperiodic systems. Zbl 1534.65273 Jiang, Kai; Li, Shifeng; Zhang, Pingwen 2 2024 On the convergence of Sobolev gradient flow for the Gross-Pitaevskii eigenvalue problem. Zbl 1535.65270 Chen, Ziang; Lu, Jianfeng; Lu, Yulong; Zhang, Xiangxiong 2 2024 wPINNs: weak physics informed neural networks for approximating entropy solutions of hyperbolic conservation laws. Zbl 1535.65249 De Ryck, Tim; Mishra, Siddhartha; Molinaro, Roberto 2 2024 An explicit and symmetric exponential wave integrator for the nonlinear Schrödinger equation with low regularity potential and nonlinearity. Zbl 07899522 Bao, Weizhu; Wang, Chushan 1 2024 Space-time finite element methods for distributed optimal control of the wave equation. Zbl 1532.49031 Löscher, Richard; Steinbach, Olaf 1 2024 A positive and moment-preserving Fourier spectral method. Zbl 1534.65257 Cai, Zhenning; Lin, Bo; Lin, Meixia 1 2024 High order splitting methods for SDEs satisfying a commutativity condition. Zbl 1532.60152 Foster, James M.; dos Reis, Gonçalo; Strange, Calum 1 2024 A universal median quasi-Monte Carlo integration. Zbl 07813245 Goda, Takashi; Suzuki, Kosuke; Matsumoto, Makoto 1 2024 A numerical framework for nonlinear peridynamics on two-dimensional manifolds based on implicit P-(EC)\(^k\) schemes. Zbl 1534.74003 Coclite, Alessandro; Coclite, Giuseppe M.; Maddalena, Francesco; Politi, Tiziano 1 2024 Generalized dimension truncation error analysis for high-dimensional numerical integration: lognormal setting and beyond. Zbl 07836940 Guth, Philipp A.; Kaarnioja, Vesa 1 2024 A posteriori error control for fourth-order semilinear problems with quadratic nonlinearity. Zbl 1541.65145 Carstensen, Carsten; Gräßle, Benedikt; Nataraj, Neela 1 2024 Singularity swapping method for nearly singular integrals based on trapezoidal rule. Zbl 1537.65178 Bao, Gang; Hua, Wenmao; Lai, Jun; Zhang, Jinrui 1 2024 Learning high-dimensional McKean-Vlasov forward-backward stochastic differential equations with general distribution dependence. Zbl 07794520 Han, Jiequn; Hu, Ruimeng; Long, Jihao 1 2024 Asymptotic-preserving and energy stable dynamical low-rank approximation. Zbl 07794523 Einkemmer, Lukas; Hu, Jingwei; Kusch, Jonas 1 2024 Total variation error bounds for the accelerated exponential Euler scheme approximation of parabolic semilinear SPDEs. Zbl 07870732 Bréhier, Charles-Edouard 1 2024 Inverse wave-number-dependent source problems for the Helmholtz equation. Zbl 07870734 Guo, Hongxia; Hu, Guanghui 1 2024 A kernel machine learning for inverse source and scattering problems. Zbl 07870737 Meng, Shixu; Zhang, Bo 1 2024 Accurately recover global quasiperiodic systems by finite points. Zbl 07892759 Jiang, Kai; Zhou, Qi; Zhang, Pingwen 1 2024 Uniform substructuring preconditioners for high order FEM on triangles and the influence of nodal basis functions. Zbl 07882246 Ainsworth, Mark; Jiang, Shuai 1 2024 Robust DPG test spaces and fortin operators – the \(H^1\) and \(\boldsymbol{H}(\operatorname{div})\) cases. Zbl 1535.65278 Führer, Thomas; Heuer, Norbert 1 2024 On optimal cell average decomposition for high-order bound-preserving schemes of hyperbolic conservation laws. Zbl 07821073 Cui, Shumo; Ding, Shengrong; Wu, Kailiang 1 2024 Error analysis of a first-order IMEX scheme for the logarithmic Schrödinger equation. Zbl 1531.65267 Wang, Li-Lian; Yan, Jingye; Zhang, Xiaolong 1 2024 Geometric two-scale integrators for highly oscillatory system: uniform accuracy and near conservations. Zbl 1517.65128 Wang, Bin; Zhao, Xiaofei 11 2023 Adaptive VEM: stabilization-free a posteriori error analysis and contraction property. Zbl 1512.65258 Beirão da Veiga, L.; Canuto, C.; Nochetto, R. H.; Vacca, G.; Verani, M. 10 2023 Discrete gradient structure of a second-order variable-step method for nonlinear integro-differential models. Zbl 1527.35452 Liao, Hong-lin; Liu, Nan; Lyu, Pin 9 2023 A new thermodynamically compatible finite volume scheme for magnetohydrodynamics. Zbl 07670867 Busto, Saray; Dumbser, Michael 9 2023 Analysis of error localization of Chebyshev spectral approximations. Zbl 1528.41016 Wang, Haiyong 8 2023 Rank-adaptive time integration of tree tensor networks. Zbl 1511.65064 Ceruti, Gianluca; Lubich, Christian; Sulz, Dominik 8 2023 Summation-by-parts operators for general function spaces. Zbl 1529.65066 Glaubitz, Jan; Nordström, Jan; Öffner, Philipp 7 2023 Wavenumber explicit convergence of a multiscale generalized finite element method for heterogeneous Helmholtz problems. Zbl 1517.65085 Chupeng, Ma; Alber, Christian; Scheichl, Robert 6 2023 A symmetrized parametric finite element method for anisotropic surface diffusion of closed curves. Zbl 1512.65205 Bao, Weizhu; Jiang, Wei; Li, Yifei 6 2023 The mpEDMD algorithm for data-driven computations of measure-preserving dynamical systems. Zbl 1517.65038 Colbrook, Matthew J. 5 2023 Exponential convergence of deep operator networks for elliptic partial differential equations. Zbl 1519.35088 Marcati, Carlo; Schwab, Christoph 5 2023 A local discontinuous Galerkin approximation for the \(p\)-Navier-Stokes system. I: Convergence analysis. Zbl 1518.76035 Kaltenbach, Alex; RůžIčka, Michael 5 2023 \(H^1\)-norm stability and convergence of an L2-type method on nonuniform meshes for subdiffusion equation. Zbl 07744121 Quan, Chaoyu; Wu, Xu 4 2023 Optimization and convergence of numerical attractors for discrete-time quasi-linear lattice system. Zbl 1512.65161 Li, Yangrong; Yang, Shuang; Caraballo, Tomás 4 2023 Optimal \(L^2\) error estimates of unconditionally stable finite element schemes for the Cahn-Hilliard-Navier-Stokes system. Zbl 1529.65057 Cai, Wentao; Sun, Weiwei; Wang, Jilu; Yang, Zongze 4 2023 Direct guaranteed lower eigenvalue bounds with optimal a priori convergence rates for the bi-Laplacian. Zbl 1521.65118 Carstensen, Carsten; Puttkammer, Sophie 4 2023 A local discontinuous Galerkin approximation for the \(p\) -Navier-Stokes system. II: Convergence rates for the velocity. Zbl 1518.76036 Kaltenbach, Alex; Růžička, Michael 4 2023 Convergence of a decoupled splitting scheme for the Cahn-Hilliard-Navier-Stokes system. Zbl 1528.65077 Liu, Chen; Masri, Rami; Riviere, Beatrice 4 2023 Provably positive central discontinuous Galerkin schemes via geometric quasilinearization for ideal MHD equations. Zbl 1516.65102 Wu, Kailiang; Jiang, Haili; Shu, Chi-Wang 4 2023 A unifying framework for interpolatory \(\mathcal{L}_2\)-optimal reduced-order modeling. Zbl 1523.30048 Mlinarić, Petar; Gugercin, Serkan 3 2023 Dispersion analysis of CIP-FEM for the Helmholtz equation. Zbl 1529.65134 Zhou, Yu; Wu, Haijun 3 2023 Suboptimality of Gauss-Hermite quadrature and optimality of the trapezoidal rule for functions with finite smoothness. Zbl 1516.65018 Kazashi, Yoshihito; Suzuki, Yuya; Goda, Takashi 3 2023 Twofold saddle-point formulation of Biot poroelasticity with stress-dependent diffusion. Zbl 1531.65237 Gómez-Vargas, Bryan; Mardal, Kent-André; Ruiz-Baier, Ricardo; Vinje, Vegard 3 2023 Analysis of a filtered time-stepping finite element method for natural convection problems. Zbl 1515.65251 Wu, Jilian; Li, Ning; Feng, Xinlong 3 2023 Fluid-fluid interaction problems at high Reynolds numbers: reducing the modeling error with LES-C. Zbl 1520.76042 Aggul, Mustafa; Labovsky, Alexander E.; Onal, Eda; Schwiebert, Kyle J. 3 2023 An exponential spectral method using VP means for semilinear subdiffusion equations with rough data. Zbl 1529.65102 Li, Buyang; Lin, Yanping; Ma, Shu; Rao, Qiqi 3 2023 High-order BDF convolution quadrature for subdiffusion models with a singular source term. Zbl 1537.65117 Shi, Jiankang; Chen, Minghua 3 2023 Difference finite element method for the 3D steady Navier-Stokes equations. Zbl 1511.76053 Feng, Xinlong; Lu, Xiaoli; He, Yinnian 3 2023 Agglomeration-based geometric multigrid schemes for the virtual element method. 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Zbl 1511.65019 Gilbert, Alexander D.; Kuo, Frances Y.; Sloan, Ian H. 1 2023 Observable error bounds of the time-splitting scheme for quantum-classical molecular dynamics. Zbl 1518.35565 Fang, Di; Vilanova, Albert Tres 1 2023 Log orthogonal functions in semi-infinite intervals: approximation results and applications. Zbl 1512.65278 Chen, Sheng; Shen, Jie 1 2023 Adaptive finite element approximations for elliptic problems using regularized forcing data. Zbl 1515.65292 Heltai, Luca; Lei, Wenyu 1 2023 Preintegration via active subspace. Zbl 1511.65008 Liu, Sifan; Owen, Art B. 1 2023 On the error rate of importance sampling with randomized quasi-Monte Carlo. Zbl 1511.65007 He, Zhijian; Zheng, Zhan; Wang, Xiaoqun 1 2023 Projection methods for neural field equations. Zbl 1520.65082 Avitabile, Daniele 1 2023 Nonlinear eigenvalue methods for linear pointwise stability of nonlinear waves. Zbl 1510.65101 Scheel, Arnd 1 2023 Generalized SAV-exponential integrator schemes for Allen-Cahn type gradient flows. Zbl 07572361 Ju, Lili; Li, Xiao; Qiao, Zhonghua 31 2022 ...and 1742 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 57,425 Authors 233 Dehghan Takht Fooladi, Mehdi 233 Shu, Chi-Wang 206 He, Yinnian 171 Chen, Yanping 169 Shi, Dongyang 168 Huang, Yunqing 159 Argyros, Ioannis Konstantinos 158 Zhang, Zhimin 147 Carstensen, Carsten 140 Schwab, Christoph 137 Wang, Hong 135 Rui, Hongxing 133 Shen, Jie 128 Simos, Theodore E. 126 Feng, Xinlong 124 Liu, Fawang 124 Zhang, Shangyou 119 Gatica, Gabriel N. 116 Burman, Erik 112 Gunzburger, Max D. 108 Cockburn, Bernardo 108 Dumbser, Michael 107 Quarteroni, Alfio M. 106 Chung, Tsz Shun Eric 106 Yang, Xiaofeng 104 Du, Qiang 103 Gander, Martin Jakob 101 Ern, Alexandre 101 Wheeler, Mary Fanett 100 Ye, Xiu 97 Beirão da Veiga, Lourenço 96 Wei, Yimin 95 Babuška, Ivo 95 Nochetto, Ricardo Horacio 95 Xu, Da 94 Hou, Yanren 94 Jackiewicz, Zdzislaw 93 Karniadakis, George Em 93 Li, Hong 92 Jiang, Yaolin 91 Huang, Chengming 91 Li, Jichun 90 Brenner, Susanne Cecelia 90 Chen, Zhangxin 90 Demkowicz, Leszek 90 Evans, David John 90 Nordström, Jan 88 Wohlmuth, Barbara I. 87 Praetorius, Dirk 86 Huang, Ting-Zhu 86 Rebholz, Leo Gregory 85 Axelsson, Axel Owe Holger 85 Osher, Stanley Joel 85 Xu, Jinchao 84 Sun, Shuyu 83 Hughes, Thomas J. 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