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: 6,093 Publications (since 1966) References Indexed: 1,253 Publications with 44,978 References. all top 5 Latest Issues 63, No. 1 (2025) 62, No. 6 (2024) 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) ...and 153 more Volumes all top 5 Authors 41 Carstensen, Carsten 37 Manteuffel, Thomas A. 37 Wheeler, Mary Fanett 36 Babuška, Ivo 35 Du, Qiang 32 Shu, Chi-Wang 31 Cockburn, Bernardo 31 Nochetto, Ricardo Horacio 31 Shen, Jie 29 Cai, Zhiqiang 29 McCormick, Steve Fahrney 26 Li, Buyang 26 Sloan, Ian Hugh 26 Sun, Weiwei 25 Schwab, Christoph 24 Gunzburger, Max Donald 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 Tadmor, Eitan 20 Widlund, Olof B. 19 Osher, Stanley Joel 19 Starke, Gerhard 19 Zhang, Zhimin 18 Wohlmuth, Barbara I. 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 Bao, Weizhu 15 Bernardi, Christine 15 Dahmen, Wolfgang A. 15 Prohl, Andreas 15 Tang, Tao 15 Thomée, Vidar 14 Atkinson, Kendall Eugene 14 Barrett, John William 14 Brunner, Hermann 14 Dawson, Clint N. 14 Demkowicz, Leszek 14 Gander, Martin Jakob 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 Stuart, Andrew M. 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 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 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 5,389 more Authors all top 5 Fields 5,498 Numerical analysis (65-XX) 2,427 Partial differential equations (35-XX) 785 Fluid mechanics (76-XX) 477 Approximations and expansions (41-XX) 451 Ordinary differential equations (34-XX) 274 Mechanics of deformable solids (74-XX) 268 Calculus of variations and optimal control; optimization (49-XX) 252 Integral equations (45-XX) 222 Probability theory and stochastic processes (60-XX) 181 Optics, electromagnetic theory (78-XX) 181 Operations research, mathematical programming (90-XX) 163 Operator theory (47-XX) 151 Statistical mechanics, structure of matter (82-XX) 136 Linear and multilinear algebra; matrix theory (15-XX) 112 Dynamical systems and ergodic theory (37-XX) 100 Computer science (68-XX) 79 Harmonic analysis on Euclidean spaces (42-XX) 70 Functional analysis (46-XX) 66 Biology and other natural sciences (92-XX) 63 Systems theory; control (93-XX) 57 Functions of a complex variable (30-XX) 56 Real functions (26-XX) 54 Special functions (33-XX) 54 Statistics (62-XX) 46 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) 35 Mechanics of particles and systems (70-XX) 30 Integral transforms, operational calculus (44-XX) 24 Number theory (11-XX) 24 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 Measure and integration (28-XX) 4 Algebraic topology (55-XX) 3 Group theory and generalizations (20-XX) 3 Topological groups, Lie groups (22-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 5,754 Publications have been cited 167,539 times in 80,091 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 1,508 2002 The local discontinuous Galerkin method for time-dependent convection-diffusion systems. Zbl 0927.65118 Cockburn, Bernardo; Shu, Chi-Wang 1,161 1998 On the construction and comparison of difference schemes. Zbl 0184.38503 Strang, Gilbert 1,034 1968 Splitting algorithms for the sum of two nonlinear operators. Zbl 0426.65050 Lions, Pierre-Louis; Mercier, B. 888 1979 An interior penalty finite element method with discontinuous elements. Zbl 0482.65060 Arnold, Douglas N. 776 1982 High resolution schemes using flux limiters for hyperbolic conservation laws. Zbl 0565.65048 Sweby, P. K. 727 1984 The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. Zbl 0811.65083 LeVeque, Randall J.; Li, Zhilin 719 1994 Unified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems. Zbl 1205.65312 Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Lazarov, Raytcho 666 2009 A convergent adaptive algorithm for Poisson’s equation. Zbl 0854.65090 Dörfler, Willy 656 1996 Inexact Newton methods. Zbl 0478.65030 Dembo, Ron S.; Eisenstat, Stanley C.; Steihaug, Trond 571 1982 A nonmonotone line search technique for Newton’s method. Zbl 0616.65067 Grippo, L.; Lampariello, F.; Lucidi, S. 566 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 563 2017 Solution of sparse indefinite systems of linear equations. Zbl 0319.65025 Paige, C. C.; Saunders, M. A. 546 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 546 1990 Error estimates for adaptive finite element computations. Zbl 0398.65069 Babuška, Ivo; Rheinboldt, W. C. 530 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 490 1982 Implicit-explicit methods for time-dependent partial differential equations. Zbl 0841.65081 Ascher, Uri M.; Ruuth, Steven J.; Wetton, Brian T. R. 485 1995 Two-grid discretization techniques for linear and nonlinear PDEs. Zbl 0860.65119 Xu, Jinchao 478 1996 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. 474 1982 A space-time spectral method for the time fractional diffusion equation. Zbl 1193.35243 Li, Xianjuan; Xu, Chuanju 458 2009 A stochastic collocation method for elliptic partial differential equations with random input data. Zbl 1151.65008 Babuška, Ivo; Nobile, Fabio; Tempone, Raúl 456 2007 Galerkin finite element approximations of stochastic elliptic partial differential equations. Zbl 1080.65003 Babuska, Ivo; Tempone, Raúl; Zouraris, Georgios E. 416 2004 An elliptic collocation-finite element method with interior penalties. Zbl 0384.65058 Wheeler, Mary Fanett 398 1978 A sparse grid stochastic collocation method for partial differential equations with random input data. Zbl 1176.65137 Nobile, F.; Tempone, R.; Webster, C. G. 392 2008 Strong convergence of Euler-type methods for nonlinear stochastic differential equations. Zbl 1026.65003 Higham, Desmond J.; Mao, Xuerong; Stuart, Andrew M. 373 2002 Uniformly high-order accurate nonoscillatory schemes. I. Zbl 0627.65102 Harten, Ami; Osher, Stanley 364 1987 The rotation of eigenvectors by a perturbation. III. Zbl 0198.47201 Davis, Chandler; Kahan, W. M. 361 1970 Virtual elements for linear elasticity problems. Zbl 1268.74010 Beirao da Veiga, L.; Brezzi, F.; Marini, L. D. 341 2013 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 339 2009 Coupling fluid flow with porous media flow. Zbl 1037.76014 Layton, William J.; Schieweck, Friedhelm; Yotov, Ivan 336 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. 333 2005 High-resolution conservative algorithms for advection in incompressible flow. Zbl 0852.76057 LeVeque, Randall J. 328 1996 A well-balanced scheme for the numerical processing of source terms in hyperbolic equations. Zbl 0876.65064 Greenberg, James M.; Le Roux, Alain-Yves 320 1996 On the \(O(1/n)\) convergence rate of the Douglas-Rachford alternating direction method. Zbl 1245.90084 He, Bingsheng; Yuan, Xiaoming 318 2012 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. 313 2009 A new class of optimal high-order strong-stability-preserving time discretization methods. Zbl 1020.65064 Spiteri, Raymond J.; Ruuth, Steven J. 303 2002 Stability theory for systems of inequalities. II: Differentiable nonlinear systems. Zbl 0347.90050 Robinson, Stephen M. 303 1976 Variational iterative methods for nonsymmetric systems of linear equations. Zbl 0524.65019 Eisenstat, Stanley C.; Elman, Howard C.; Schultz, Martin H. 302 1983 High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations. Zbl 0736.65066 Osher, Stanley; Shu, Chi-Wang 298 1991 On Krylov subspace approximations to the matrix exponential operator. Zbl 0888.65032 Hochbruck, Marlis; Lubich, Christian 297 1997 A priori \(L_2\) error estimates for Galerkin approximations to parabolic partial differential equations. Zbl 0232.35060 Wheeler, Mary Fanett 297 1972 Sharp error estimate of the nonuniform L1 formula for linear reaction-subdiffusion equations. Zbl 1447.65026 Liao, Hong-lin; Li, Dongfang; Zhang, Jiwei 291 2018 Poincaré–Friedrichs inequalities for piecewise \(H^{1}\) functions. Zbl 1045.65100 Brenner, Susanne C. 289 2003 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. 289 2012 On Godunov-type methods for gas dynamics. Zbl 0642.76088 Einfeldt, Bernd 277 1988 An algorithm for generalized matrix eigenvalue problems. Zbl 0253.65019 Moler, C. B.; Stewart, G. W. 276 1973 Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics. Zbl 1075.65118 Kunisch, K.; Volkwein, S. 276 2002 Diagonally implicit Runge-Kutta methods for stiff O.D.E.’s. Zbl 0374.65038 Alexander, Roger 274 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. 274 2008 Inexact and preconditioned Uzawa algorithms for saddle point problems. Zbl 0815.65041 Elman, Howard C.; Golub, Gene H. 271 1994 Stabilization of low-order mixed finite elements for the Stokes equations. Zbl 1145.76015 Bochev, Pavel B.; Dohrmann, Clark R.; Gunzburger, Max D. 271 2006 Image selective smoothing and edge detection by nonlinear diffusion. Zbl 0746.65091 Catté, Francine; Lions, Pierre-Louis; Morel, Jean-Michel; Coll, Tomeu 267 1992 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 266 2000 Error estimate procedure in the finite element method and applications. Zbl 0582.65078 Ladeveze, P.; Leguillon, D. 264 1983 Discontinuous \(hp\)-finite element methods for advection-diffusion-reaction problems. Zbl 1015.65067 Houston, Paul; Schwab, Christoph; Süli, Endre 252 2002 Some error estimates for the box method. Zbl 0634.65105 Bank, Randolph E.; Rose, Donald J. 251 1987 Numerical methods for nonconservative hyperbolic systems: A theoretical framework. Zbl 1130.65089 Parés, Carlos 250 2006 Nested dissection of a regular finite element mesh. Zbl 0259.65087 George, Alan 250 1973 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. 248 2014 On direct methods for solving Poisson’s equations. Zbl 0217.52902 Buzbee, B. L.; Golub, G. H.; Nielson, C. W. 246 1970 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. 245 1994 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. 242 2008 Stability analysis of large time-stepping methods for epitaxial growth models. Zbl 1127.65069 Xu, Chuanju; Tang, Tao 239 2006 Explicit exponential Runge-Kutta methods for semilinear parabolic problems. Zbl 1093.65052 Hochbruck, Marlis; Ostermann, Alexander 238 2005 Analysis of the inexact Uzawa algorithm for saddle point problems. Zbl 0873.65031 Bramble, James H.; Pasciak, Joseph E.; Vassilev, Apostol T. 235 1997 Adaptive finite element methods for parabolic problems. I: A linear model problem. Zbl 0732.65093 Eriksson, Kenneth; Johnson, Claes 235 1991 Analysis of some Krylov subspace approximations to the matrix exponential operator. Zbl 0749.65030 Saad, Y. 233 1992 Monotone piecewise cubic interpolation. Zbl 0423.65011 Fritsch, F. N.; Carlson, R. E. 230 1980 A mortar finite element method using dual spaces for the Lagrange multiplier. Zbl 0974.65105 Wohlmuth, Barbara I. 230 2000 The conjugate gradient method and trust regions in large scale optimization. Zbl 0518.65042 Steihaug, Trond 225 1983 A posteriori error estimates for a discontinuous Galerkin approximation of second-order elliptic problems. Zbl 1058.65120 Karakashian, Ohannes A.; Pascal, Frederic 225 2003 Collocation at Gaussian points. Zbl 0232.65065 de Boor, Carl; Swartz, Blair 223 1973 Data oscillation and convergence of adaptive FEM. Zbl 0970.65113 Morin, Pedro; Nochetto, Ricardo H.; Siebert, Kunibert G. 223 2000 A discrete Grönwall inequality with applications to numerical schemes for subdiffusion problems. Zbl 1414.65008 Liao, Hong-lin; McLean, William; Zhang, Jiwei 220 2019 An energy stable and convergent finite-difference scheme for the modified phase field crystal equation. Zbl 1230.82005 Wang, C.; Wise, S. M. 219 2011 A local discontinuous Galerkin method for KdV type equations. Zbl 1021.65050 Yan, Jue; Shu, Chi-Wang 219 2002 Convergence and error analysis for the scalar auxiliary variable (SAV) schemes to gradient flows. Zbl 1403.65047 Shen, Jie; Xu, Jie 217 2018 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. 216 2008 Iterative solution of implicit approximations of multidimensional partial differential equations. Zbl 0197.13304 Stone, H. L. 215 1968 Optimized Schwarz methods. Zbl 1117.65165 Gander, Martin J. 214 2006 An analysis of the total least squares problem. Zbl 0468.65011 Golub, Gene H.; Van Loan, Charles F. 210 1980 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 Mixed finite elements for elliptic problems with tensor coefficients as cell-centered finite differences. Zbl 0880.65084 Arbogast, Todd; Wheeler, Mary F.; Yotov, Ivan 209 1997 The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate. Zbl 0258.65045 Golub, G. H.; Pereyra, V. 208 1973 Mean-square and asymptotic stability of the stochastic theta method. Zbl 0982.60051 Higham, Desmond J. 208 2000 Stability analysis of numerical schemes for stochastic differential equations. Zbl 0869.60052 Saito, Yoshihiro; Mitsui, Taketomo 207 1996 Error estimates for a semidiscrete finite element method for fractional order parabolic equations. Zbl 1268.65126 Jin, Bangti; Lazarov, Raytcho; Zhou, Zhi 206 2013 On the angle condition in the finite element method. Zbl 0324.65046 Babuška, Ivo; Aziz, A. K. 205 1976 On the accuracy of the finite volume element method based on piecewise linear polynomials. Zbl 1036.65084 Ewing, Richard E.; Lin, Tao; Lin, Yanping 204 2002 Application of an ultra weak variational formulation of elliptic PDEs to the two-dimensional Helmholtz problem. Zbl 0955.65081 Cessenat, Olivier; Despres, Bruno 201 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 Two-level method based on finite element and Crank-Nicolson extrapolation for the time-dependent Navier-Stokes equations. Zbl 1130.76365 He, Yinnian 198 2003 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 198 2007 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 197 1997 A stream virtual element formulation of the Stokes problem on polygonal meshes. Zbl 1427.76198 Antonietti, P. F.; Beirão da Veiga, L.; Mora, D.; Verani, M. 195 2014 A family of fourth-order methods for nonlinear equations. Zbl 0266.65040 King, Richard F. 195 1973 Fundamental solutions method for elliptic boundary value problems. Zbl 0579.65121 Bogomolny, Alexander 195 1985 Convergence of the mimetic finite difference method for diffusion problems on polyhedral meshes. Zbl 1108.65102 Brezzi, Franco; Lipnikov, Konstantin; Shashkov, Mikhail 194 2005 The global dynamics of discrete semilinear parabolic equations. Zbl 0792.65066 Elliott, C. M.; Stuart, A. M. 193 1993 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 Analysis and numerical approximation of stationary second-order mean field game partial differential inclusions. Zbl 1531.91010 Osborne, Yohance A. P.; Smears, Iain 5 2024 On uncertainty quantification of eigenvalues and eigenspaces with higher multiplicity. Zbl 07805447 Dölz, Jürgen; Ebert, David 5 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 4 2024 On optimal cell average decomposition for high-order bound-preserving schemes of hyperbolic conservation laws. Zbl 07821073 Cui, Shumo; Ding, Shengrong; Wu, Kailiang 4 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 4 2024 Asymptotic-preserving and energy stable dynamical low-rank approximation. Zbl 1543.65053 Einkemmer, Lukas; Hu, Jingwei; Kusch, Jonas 3 2024 Space-time virtual elements for the heat equation. Zbl 1539.65117 Gomez, Sergio; Mascotto, Lorenzo; Moiola, Andrea; Perugia, Ilaria 3 2024 Numerical methods and analysis of computing quasiperiodic systems. Zbl 1534.65273 Jiang, Kai; Li, Shifeng; Zhang, Pingwen 3 2024 Space-time finite element methods for distributed optimal control of the wave equation. Zbl 1532.49031 Löscher, Richard; Steinbach, Olaf 3 2024 Learning high-dimensional McKean-Vlasov forward-backward stochastic differential equations with general distribution dependence. Zbl 07794520 Han, Jiequn; Hu, Ruimeng; Long, Jihao 2 2024 Algebraic structure of the weak stage order conditions for Runge-Kutta methods. Zbl 1537.65084 Biswas, Abhijit; Ketcheson, David; Seibold, Benjamin; Shirokoff, David 2 2024 Bilinear optimal control for the fractional Laplacian: analysis and discretization. Zbl 07870733 Bersetche, Francisco; Fuica, Francisco; Otárola, Enrique; Quero, Daniel 2 2024 Inverse wave-number-dependent source problems for the Helmholtz equation. Zbl 07870734 Guo, Hongxia; Hu, Guanghui 2 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 2 2024 Structure preserving primal dual methods for gradient flows with nonlinear mobility transport distances. Zbl 1534.65091 Carrillo, José A.; Wang, Li; Wei, Chaozhen 2 2024 Contraction and convergence rates for discretized kinetic Langevin dynamics. Zbl 1545.65011 Leimkuhler, Benedict J.; Paulin, Daniel; Whalley, Peter A. 2 2024 Accurately recover global quasiperiodic systems by finite points. Zbl 07892759 Jiang, Kai; Zhou, Qi; Zhang, Pingwen 2 2024 Polynomial interpolation of function averages on interval segments. Zbl 1542.41001 Bruni Bruno, Ludovico; Erb, Wolfgang 2 2024 Lattice Green’s functions for high-order finite difference stencils. Zbl 1531.31007 Gabbard, James; van Rees, Wim M. 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 Total variation error bounds for the accelerated exponential Euler scheme approximation of parabolic semilinear SPDEs. Zbl 1545.65029 Bréhier, Charles-Edouard 1 2024 Error bounds for discrete minimizers of the Ginzburg-Landau energy in the high-\(\kappa\) regime. Zbl 1542.65157 Dörich, Benjamin; Henning, Patrick 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 Virtual element methods without extrinsic stabilization. Zbl 1534.65233 Chen, Chunyu; Huang, Xuehai; Wei, Huayi 1 2024 Numerical analysis for convergence of a sample-wise backpropagation method for training stochastic neural networks. Zbl 1534.65019 Archibald, Richard; Bao, Feng; Cao, Yanzhao; Sun, Hui 1 2024 Homogenization of nondivergence-form elliptic equations with discontinuous coefficients and finite element approximation of the homogenized problem. Zbl 1534.35017 Sprekeler, Timo 1 2024 Convergence analysis for Bregman iterations in minimizing a class of Landau free energy functionals. Zbl 1534.65084 Bao, Chenglong; Chen, Chang; Jiang, Kai; Qiu, Lingyun 1 2024 An adaptive spectral method for oscillatory second-order linear ODEs with frequency-independent cost. Zbl 1534.65112 Agocs, Fruzsina J.; Barnett, Alex H. 1 2024 A positive and moment-preserving Fourier spectral method. Zbl 1534.65257 Cai, Zhenning; Lin, Bo; Lin, Meixia 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 Generalized dimension truncation error analysis for high-dimensional numerical integration: lognormal setting and beyond. Zbl 1542.65029 Guth, Philipp A.; Kaarnioja, Vesa 1 2024 Cut finite element method for divergence-free approximation of incompressible flow: a Lagrange multiplier approach. Zbl 1540.65477 Burman, Erik; Hansbo, Peter; Larson, Mats 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 A kernel machine learning for inverse source and scattering problems. Zbl 07870737 Meng, Shixu; Zhang, Bo 1 2024 Mean dimension of radial basis functions. Zbl 07862222 Hoyt, Christopher; Owen, Art B. 1 2024 Pointwise gradient estimate of the Ritz projection. Zbl 1540.65482 Diening, Lars; Rolfes, Julian; Salgado, Abner J. 1 2024 Analytic and Gevrey class regularity for parametric elliptic eigenvalue problems and applications. Zbl 1545.65413 Chernov, Alexey; Lê, Tùng 1 2024 An explicit and symmetric exponential wave integrator for the nonlinear Schrödinger equation with low regularity potential and nonlinearity. Zbl 1545.35170 Bao, Weizhu; Wang, Chushan 1 2024 Positivity preserving and mass conservative projection method for the Poisson-Nernst-Planck equation. Zbl 1544.65143 Tong, Fenghua; Cai, Yongyong 1 2024 A convergent evolving finite element method with artificial tangential motion for surface evolution under a prescribed velocity field. Zbl 07930210 Bai, Genming; Hu, Jiashun; Li, Buyang 1 2024 Uniform substructuring preconditioners for high order FEM on triangles and the influence of nodal basis functions. Zbl 1544.65200 Ainsworth, Mark; Jiang, Shuai 1 2024 On a new class of BDF and IMEX schemes for parabolic type equations. Zbl 1544.65155 Huang, Fukeng; Shen, Jie 1 2024 Finite element discretization of the steady, generalized Navier-Stokes equations with inhomogeneous Dirichlet boundary conditions. Zbl 1547.35299 Jeßberger, Julius; Kaltenbach, Alex 1 2024 New time domain decomposition methods for parabolic optimal control problems. I: Dirichlet-Neumann and Neumann-Dirichlet algorithms. Zbl 1544.65165 Gander, Martin J.; Lu, Liu-Di 1 2024 Erratum to: “Analysis and numerical approximation of stationary second-order mean field game partial differential inclusions”. Zbl 07939048 Osborne, Yohance A. P.; Smears, Iain 1 2024 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 14 2023 Geometric two-scale integrators for highly oscillatory system: uniform accuracy and near conservations. Zbl 1517.65128 Wang, Bin; Zhao, Xiaofei 12 2023 A new thermodynamically compatible finite volume scheme for magnetohydrodynamics. Zbl 07670867 Busto, Saray; Dumbser, Michael 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. 11 2023 Rank-adaptive time integration of tree tensor networks. Zbl 1511.65064 Ceruti, Gianluca; Lubich, Christian; Sulz, Dominik 9 2023 Analysis of error localization of Chebyshev spectral approximations. Zbl 1528.41016 Wang, Haiyong 9 2023 Wavenumber explicit convergence of a multiscale generalized finite element method for heterogeneous Helmholtz problems. Zbl 1517.65085 Chupeng, Ma; Alber, Christian; Scheichl, Robert 9 2023 A symmetrized parametric finite element method for anisotropic surface diffusion of closed curves. Zbl 1512.65205 Bao, Weizhu; Jiang, Wei; Li, Yifei 8 2023 The mpEDMD algorithm for data-driven computations of measure-preserving dynamical systems. Zbl 1517.65038 Colbrook, Matthew J. 8 2023 Optimization and convergence of numerical attractors for discrete-time quasi-linear lattice system. Zbl 1512.65161 Li, Yangrong; Yang, Shuang; Caraballo, Tomás 7 2023 Provably positive central discontinuous Galerkin schemes via geometric quasilinearization for ideal MHD equations. Zbl 1516.65102 Wu, Kailiang; Jiang, Haili; Shu, Chi-Wang 7 2023 Exponential convergence of deep operator networks for elliptic partial differential equations. Zbl 1519.35088 Marcati, Carlo; Schwab, Christoph 6 2023 Summation-by-parts operators for general function spaces. Zbl 1529.65066 Glaubitz, Jan; Nordström, Jan; Öffner, Philipp 6 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. 6 2023 Difference finite element method for the 3D steady Navier-Stokes equations. Zbl 1511.76053 Feng, Xinlong; Lu, Xiaoli; He, Yinnian 6 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 6 2023 A local discontinuous Galerkin approximation for the \(p\)-Navier-Stokes system. I: Convergence analysis. Zbl 1518.76035 Kaltenbach, Alex; RůžIčka, Michael 6 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 6 2023 Agglomeration-based geometric multigrid schemes for the virtual element method. Zbl 1512.65290 Antonietti, Paola F.; Berrone, Stefano; Busetto, Martina; Verani, Marco 5 2023 Analysis of a filtered time-stepping finite element method for natural convection problems. Zbl 1515.65251 Wu, Jilian; Li, Ning; Feng, Xinlong 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 5 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 High-order BDF convolution quadrature for subdiffusion models with a singular source term. Zbl 1537.65117 Shi, Jiankang; Chen, Minghua 4 2023 POD-ROMs for incompressible flows including snapshots of the temporal derivative of the full order solution. Zbl 1516.65086 García-Archilla, Bosco; John, Volker; Novo, Julia 4 2023 A kernel-based least-squares collocation method for surface diffusion. Zbl 1531.65264 Chen, Meng; Cheung, Ka Chun; Ling, Leevan 4 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 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 Error estimation of the relaxation finite difference scheme for the nonlinear Schrödinger equation. Zbl 1529.65022 Zouraris, Georgios E. 4 2023 A local discontinuous Galerkin approximation for the \(p\)-Navier-Stokes system. III: Convergence rates for the pressure. Zbl 1518.76037 Kaltenbach, Alex; Růžička, Michael 4 2023 Resolution of singularities by rational functions. Zbl 1535.65049 Herremans, Astrid; Huybrechs, Daan; Trefethen, Lloyd N. 3 2023 An energy stable and maximum bound principle preserving scheme for the dynamic Ginzburg-Landau equations under the temporal gauge. Zbl 07770182 Ma, Limin; Qiao, Zhonghua 3 2023 Relaxed Kačanov scheme for the \(p\)-Laplacian with large exponent. Zbl 1529.35259 Balci, Anna Kh.; Diening, Lars; Storn, Johannes 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 Ensemble domain decomposition algorithm for the fully mixed random Stokes-Darcy model with the Beavers-Joseph interface conditions. Zbl 1549.65531 Shi, Feng; Sun, Yizhong; Zheng, Haibiao 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 Convergence analysis of Newton-Schur method for symmetric elliptic eigenvalue problem. Zbl 1519.65051 Shao, Nian; Chen, Wenbin 3 2023 On the error rate of importance sampling with randomized quasi-Monte Carlo. Zbl 1511.65007 He, Zhijian; Zheng, Zhan; Wang, Xiaoqun 3 2023 Computational lower bounds of the Maxwell eigenvalues. Zbl 1518.35581 Gallistl, Dietmar; Olkhovskiy, Vladislav 3 2023 Erratum to: “Convergence of Dziuk’s semidiscrete finite element method for mean curvature flow of closed surfaces with high-order finite elements”. Zbl 1526.65043 Bai, Genming; Li, Buyang 3 2023 Gauge-transformed exponential integrator for generalized KdV equations with rough data. Zbl 07713540 Li, Bing; Wu, Yifei; Zhao, Xiaofei 3 2023 \(p\)-robust equilibrated flux reconstruction in \(\boldsymbol{H}(\mathrm{curl})\) based on local minimizations: application to a posteriori analysis of the curl-curl problem. Zbl 1535.65275 Chaumont-Frelet, Théophile; Vohralík, Martin 3 2023 A convexity-preserving and perimeter-decreasing parametric finite element method for the area-preserving curve shortening flow. Zbl 1522.65174 Jiang, Wei; Su, Chunmei; Zhang, Ganghui 3 2023 A unifying framework for interpolatory \(\mathcal{L}_2\)-optimal reduced-order modeling. Zbl 1523.30048 Mlinarić, Petar; Gugercin, Serkan 3 2023 Nonconforming virtual elements for the biharmonic equation with Morley degrees of freedom on polygonal meshes. Zbl 1528.65103 Carstensen, Carsten; Khot, Rekha; Pani, Amiya K. 2 2023 Exponential convergence of \(hp\)-FEM for the integral fractional Laplacian in polygons. Zbl 1533.65224 Faustmann, Markus; Marcati, Carlo; Melenk, Jens Markus; Schwab, Christoph 2 2023 A probabilistic scheme for semilinear nonlocal diffusion equations with volume constraints. Zbl 07770183 Yang, Minglei; Zhang, Guannan; Del-Castillo-Negrete, Diego; Cao, Yanzhao 2 2023 Monte Carlo gradient in optimization constrained by radiative transport equation. Zbl 1545.65012 Li, Qin; Wang, Li; Yang, Yunan 2 2023 Fast Krasnosel’skiĭ-Mann algorithm with a convergence rate of the fixed point iteration of \(o\left(\frac{1}{k}\right)\). Zbl 07770187 Boţ, Radu Ioan; Nguyen, Dang-Khoa 2 2023 Implicit-explicit time discretization for Oseen’s equation at high Reynolds number with application to fractional step methods. Zbl 1543.76077 Burman, Erik; Garg, Deepika; Guzman, Johnny 2 2023 Stability and error analysis of a second-order consistent splitting scheme for the Navier-Stokes equations. Zbl 1529.65100 Huang, Fukeng; Shen, Jie 2 2023 Discrete hyperbolic curvature flow in the plane. Zbl 1522.65139 Deckelnick, Klaus; Nürnberg, Robert 2 2023 An improved high-order method for elliptic multiscale problems. Zbl 1529.65121 Dong, Zhaonan; Hauck, Moritz; Maier, Roland 2 2023 ...and 1753 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 58,531 Authors 239 Shu, Chi-Wang 234 Dehghan Takht Fooladi, Mehdi 210 He, Yinnian 178 Chen, Yanping 174 Shi, Dongyang 170 Huang, Yunqing 162 Zhang, Zhimin 161 Argyros, Ioannis Konstantinos 149 Carstensen, Carsten 142 Schwab, Christoph 138 Wang, Hong 137 Rui, Hongxing 137 Shen, Jie 132 Feng, Xinlong 129 Simos, Theodore E. 129 Zhang, Shangyou 124 Liu, Fawang 119 Gander, Martin Jakob 119 Gatica, Gabriel N. 118 Burman, Erik 112 Dumbser, Michael 112 Gunzburger, Max Donald 109 Cockburn, Bernardo 109 Yang, Xiaofeng 108 Chung, Tsz Shun Eric 108 Quarteroni, Alfio M. 107 Du, Qiang 102 Wheeler, Mary Fanett 101 Ern, Alexandre 101 Ye, Xiu 99 Wei, Yimin 97 Beirão da Veiga, Lourenço 97 Jiang, Yaolin 96 Xu, Da 95 Babuška, Ivo 95 Jackiewicz, Zdzislaw 95 Karniadakis, George Em 95 Li, Hong 95 Nochetto, Ricardo Horacio 94 Hou, Yanren 93 Chen, Zhangxin 92 Huang, Chengming 92 Li, Jichun 91 Brenner, Susanne Cecelia 91 Demkowicz, Leszek 90 Evans, David John 90 Nordström, Jan 88 Wohlmuth, Barbara I. 87 Huang, Ting-Zhu 87 Praetorius, Dirk 87 Rebholz, Leo Gregory 86 Sun, Shuyu 86 Wang, Cheng 86 Xu, Jinchao 85 Axelsson, Axel Owe Holger 85 Osher, Stanley Joel 84 Li, Buyang 84 Manzini, Gianmarco 83 Hughes, Thomas J. 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