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: 6,002 Publications (since 1966) References Indexed: 1,162 Publications with 41,536 References. all top 5 Latest Issues 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) 46, No. 1 (2008) 45, No. 6 (2007) 45, No. 5 (2007) ...and 148 more Volumes all top 5 Authors 40 Carstensen, Carsten 37 Manteuffel, Thomas A. 37 Wheeler, Mary Fanett 36 Babuška, Ivo 34 Du, Qiang 31 Cockburn, Bernardo 31 Nochetto, Ricardo Horacio 31 Shu, Chi-Wang 29 Cai, Zhiqiang 29 McCormick, Steve Fahrney 27 Shen, Jie 26 Sloan, Ian Hugh 25 Schwab, Christoph 25 Sun, Weiwei 24 Gunzburger, Max D. 24 Li, Buyang 23 Süli, Endre E. 22 Ainsworth, Mark 22 Ewing, Richard Edward 20 Bartels, Sören 20 Burman, Erik 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. 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 17 Zhang, Zhimin 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 Beirão da Veiga, Lourenço 15 Bernardi, Christine 15 Prohl, Andreas 15 Thomée, Vidar 14 Atkinson, Kendall Eugene 14 Barrett, John William 14 Brunner, Hermann 14 Dahmen, Wolfgang A. 14 Dawson, Clint N. 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 Tang, Tao 14 Wang, Hong 14 Xu, Jinchao 14 Yotov, Ivan 13 Bao, Weizhu 13 Bialecki, Bernard 13 Burrage, Kevin 13 Conn, Andrew Roger 13 Demkowicz, Leszek F. 13 Demlow, Alan 13 Dupont, Todd F. 13 Graham, Ivan G. 13 Johnson, Claes G. L. 13 Nicolaides, Roy A. 13 Schötzau, Dominik 13 Trefethen, Lloyd Nicholas 13 Wu, Haijun 12 Ascher, Uri M. 12 Bochev, Pavel B. 12 Brenner, Susanne Cecelia 12 Chan, Tony Fan-Cheong 12 Falk, Richard S. 12 Gander, Martin Jakob 12 Heuer, Norbert 12 Jin, Shi 12 Joly, Patrick 12 Luskin, Mitchell 12 Ma, Heping 12 Novo, Julia 12 Ostermann, Alexander 12 Pareschi, Lorenzo 12 Petzold, Linda Ruth 12 Sauter, Stefan 12 Stuart, Andrew M. 11 Bramble, James H. 11 Canuto, Claudio 11 Dick, Josef ...and 5,277 more Authors all top 5 Fields 5,410 Numerical analysis (65-XX) 2,386 Partial differential equations (35-XX) 776 Fluid mechanics (76-XX) 465 Approximations and expansions (41-XX) 449 Ordinary differential equations (34-XX) 266 Mechanics of deformable solids (74-XX) 260 Calculus of variations and optimal control; optimization (49-XX) 251 Integral equations (45-XX) 219 Probability theory and stochastic processes (60-XX) 177 Optics, electromagnetic theory (78-XX) 177 Operations research, mathematical programming (90-XX) 163 Operator theory (47-XX) 146 Statistical mechanics, structure of matter (82-XX) 135 Linear and multilinear algebra; matrix theory (15-XX) 110 Dynamical systems and ergodic theory (37-XX) 92 Computer science (68-XX) 77 Harmonic analysis on Euclidean spaces (42-XX) 65 Functional analysis (46-XX) 63 Biology and other natural sciences (92-XX) 59 Systems theory; control (93-XX) 56 Functions of a complex variable (30-XX) 55 Real functions (26-XX) 52 Special functions (33-XX) 51 Statistics (62-XX) 45 Potential theory (31-XX) 43 Global analysis, analysis on manifolds (58-XX) 43 Quantum theory (81-XX) 43 Geophysics (86-XX) 42 Information and communication theory, circuits (94-XX) 39 Classical thermodynamics, heat transfer (80-XX) 37 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 5,623 Publications have been cited 152,629 times in 73,207 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 1,389 2002 The local discontinuous Galerkin method for time-dependent convection-diffusion systems. Zbl 0927.65118 Cockburn, Bernardo; Shu, Chi-Wang 1,060 1998 On the construction and comparison of difference schemes. Zbl 0184.38503 Strang, Gilbert 914 1968 Splitting algorithms for the sum of two nonlinear operators. Zbl 0426.65050 Lions, Pierre-Louis; Mercier, B. 814 1979 An interior penalty finite element method with discontinuous elements. Zbl 0482.65060 Arnold, Douglas N. 725 1982 The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. Zbl 0811.65083 LeVeque, Randall J.; Li, Zhilin 675 1994 High resolution schemes using flux limiters for hyperbolic conservation laws. Zbl 0565.65048 Sweby, P. K. 658 1984 A convergent adaptive algorithm for Poisson’s equation. Zbl 0854.65090 Dörfler, Willy 616 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 587 2009 Inexact Newton methods. Zbl 0478.65030 Dembo, Ron S.; Eisenstat, Stanley C.; Steihaug, Trond 545 1982 A nonmonotone line search technique for Newton’s method. Zbl 0616.65067 Grippo, L.; Lampariello, F.; Lucidi, S. 538 1986 Error estimates for adaptive finite element computations. Zbl 0398.65069 Babuška, Ivo; Rheinboldt, W. C. 499 1978 Solution of sparse indefinite systems of linear equations. Zbl 0319.65025 Paige, C. C.; Saunders, M. A. 485 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 464 1990 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 459 2017 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. 454 1982 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 450 1982 Implicit-explicit methods for time-dependent partial differential equations. Zbl 0841.65081 Ascher, Uri M.; Ruuth, Steven J.; Wetton, Brian T. R. 441 1995 A stochastic collocation method for elliptic partial differential equations with random input data. Zbl 1151.65008 Babuška, Ivo; Nobile, Fabio; Tempone, Raúl 423 2007 Two-grid discretization techniques for linear and nonlinear PDEs. Zbl 0860.65119 Xu, Jinchao 418 1996 A space-time spectral method for the time fractional diffusion equation. Zbl 1193.35243 Li, Xianjuan; Xu, Chuanju 418 2009 Galerkin finite element approximations of stochastic elliptic partial differential equations. Zbl 1080.65003 Babuska, Ivo; Tempone, Raúl; Zouraris, Georgios E. 388 2004 An elliptic collocation-finite element method with interior penalties. Zbl 0384.65058 Wheeler, Mary Fanett 372 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. 371 2008 Strong convergence of Euler-type methods for nonlinear stochastic differential equations. Zbl 1026.65003 Higham, Desmond J.; Mao, Xuerong; Stuart, Andrew M. 343 2002 Uniformly high-order accurate nonoscillatory schemes. I. Zbl 0627.65102 Harten, Ami; Osher, Stanley 333 1987 The rotation of eigenvectors by a perturbation. III. Zbl 0198.47201 Davis, Chandler; Kahan, W. M. 333 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. 317 2009 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. 307 2005 High-resolution conservative algorithms for advection in incompressible flow. Zbl 0852.76057 LeVeque, Randall J. 304 1996 Coupling fluid flow with porous media flow. Zbl 1037.76014 Layton, William J.; Schieweck, Friedhelm; Yotov, Ivan 304 2003 Finite element method for the space and time fractional Fokker-Planck equation. Zbl 1416.65344 Deng, Weihua 301 2009 On the \(O(1/n)\) convergence rate of the Douglas-Rachford alternating direction method. Zbl 1245.90084 He, Bingsheng; Yuan, Xiaoming 298 2012 Stability theory for systems of inequalities. II: Differentiable nonlinear systems. Zbl 0347.90050 Robinson, Stephen M. 296 1976 A well-balanced scheme for the numerical processing of source terms in hyperbolic equations. Zbl 0876.65064 Greenberg, James M.; Le Roux, Alain-Yves 288 1996 Virtual elements for linear elasticity problems. Zbl 1268.74010 Beirao da Veiga, L.; Brezzi, F.; Marini, L. D. 283 2013 A new class of optimal high-order strong-stability-preserving time discretization methods. Zbl 1020.65064 Spiteri, Raymond J.; Ruuth, Steven J. 276 2002 High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations. Zbl 0736.65066 Osher, Stanley; Shu, Chi-Wang 273 1991 Variational iterative methods for nonsymmetric systems of linear equations. Zbl 0524.65019 Eisenstat, Stanley C.; Elman, Howard C.; Schultz, Martin H. 272 1983 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. 271 2009 On Krylov subspace approximations to the matrix exponential operator. Zbl 0888.65032 Hochbruck, Marlis; Lubich, Christian 270 1997 Poincaré–Friedrichs inequalities for piecewise \(H^{1}\) functions. Zbl 1045.65100 Brenner, Susanne C. 266 2003 Quasi-optimal convergence rate for an adaptive finite element method. Zbl 1176.65122 Cascon, J. Manuel; Kreuzer, Christian; Nochetto, Ricardo H.; Siebert, Kunibert G. 259 2008 Image selective smoothing and edge detection by nonlinear diffusion. Zbl 0746.65091 Catté, Francine; Lions, Pierre-Louis; Morel, Jean-Michel; Coll, Tomeu 257 1992 A priori \(L_2\) error estimates for Galerkin approximations to parabolic partial differential equations. Zbl 0232.35060 Wheeler, Mary Fanett 256 1972 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. 254 2012 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 254 2000 Inexact and preconditioned Uzawa algorithms for saddle point problems. Zbl 0815.65041 Elman, Howard C.; Golub, Gene H. 251 1994 On Godunov-type methods for gas dynamics. Zbl 0642.76088 Einfeldt, Bernd 250 1988 Diagonally implicit Runge-Kutta methods for stiff O.D.E.’s. Zbl 0374.65038 Alexander, Roger 250 1977 Error estimate procedure in the finite element method and applications. Zbl 0582.65078 Ladeveze, P.; Leguillon, D. 247 1983 Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics. Zbl 1075.65118 Kunisch, K.; Volkwein, S. 247 2002 Discontinuous \(hp\)-finite element methods for advection-diffusion-reaction problems. Zbl 1015.65067 Houston, Paul; Schwab, Christoph; Süli, Endre 241 2002 An algorithm for generalized matrix eigenvalue problems. Zbl 0253.65019 Moler, C. B.; Stewart, G. W. 241 1973 Stabilization of low-order mixed finite elements for the Stokes equations. Zbl 1145.76015 Bochev, Pavel B.; Dohrmann, Clark R.; Gunzburger, Max D. 240 2006 Some error estimates for the box method. Zbl 0634.65105 Bank, Randolph E.; Rose, Donald J. 239 1987 Nested dissection of a regular finite element mesh. Zbl 0259.65087 George, Alan 232 1973 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. 228 1994 Sharp error estimate of the nonuniform L1 formula for linear reaction-subdiffusion equations. Zbl 1447.65026 Liao, Hong-lin; Li, Dongfang; Zhang, Jiwei 227 2018 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. 225 2008 Analysis of the inexact Uzawa algorithm for saddle point problems. Zbl 0873.65031 Bramble, James H.; Pasciak, Joseph E.; Vassilev, Apostol T. 224 1997 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. 221 2014 Adaptive finite element methods for parabolic problems. I: A linear model problem. Zbl 0732.65093 Eriksson, Kenneth; Johnson, Claes 219 1991 Monotone piecewise cubic interpolation. Zbl 0423.65011 Fritsch, F. N.; Carlson, R. E. 219 1980 On direct methods for solving Poisson’s equations. Zbl 0217.52902 Buzbee, B. L.; Golub, G. H.; Nielson, C. W. 218 1970 Data oscillation and convergence of adaptive FEM. Zbl 0970.65113 Morin, Pedro; Nochetto, Ricardo H.; Siebert, Kunibert G. 217 2000 A posteriori error estimates for a discontinuous Galerkin approximation of second-order elliptic problems. Zbl 1058.65120 Karakashian, Ohannes A.; Pascal, Frederic 215 2003 Numerical methods for nonconservative hyperbolic systems: A theoretical framework. Zbl 1130.65089 Parés, Carlos 212 2006 Stability analysis of large time-stepping methods for epitaxial growth models. Zbl 1127.65069 Xu, Chuanju; Tang, Tao 209 2006 A mortar finite element method using dual spaces for the Lagrange multiplier. Zbl 0974.65105 Wohlmuth, Barbara I. 209 2000 Analysis of some Krylov subspace approximations to the matrix exponential operator. Zbl 0749.65030 Saad, Y. 209 1992 The conjugate gradient method and trust regions in large scale optimization. Zbl 0518.65042 Steihaug, Trond 208 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. 208 2008 Collocation at Gaussian points. Zbl 0232.65065 de Boor, Carl; Swartz, Blair 208 1973 A local discontinuous Galerkin method for KdV type equations. Zbl 1021.65050 Yan, Jue; Shu, Chi-Wang 206 2002 Explicit exponential Runge-Kutta methods for semilinear parabolic problems. Zbl 1093.65052 Hochbruck, Marlis; Ostermann, Alexander 204 2005 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 201 2001 Mean-square and asymptotic stability of the stochastic theta method. Zbl 0982.60051 Higham, Desmond J. 200 2000 The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate. Zbl 0258.65045 Golub, G. H.; Pereyra, V. 196 1973 Stability analysis of numerical schemes for stochastic differential equations. Zbl 0869.60052 Saito, Yoshihiro; Mitsui, Taketomo 195 1996 On the angle condition in the finite element method. Zbl 0324.65046 Babuška, Ivo; Aziz, A. K. 194 1976 Optimized Schwarz methods. Zbl 1117.65165 Gander, Martin J. 194 2006 Iterative solution of implicit approximations of multidimensional partial differential equations. Zbl 0197.13304 Stone, H. L. 193 1968 An energy stable and convergent finite-difference scheme for the modified phase field crystal equation. Zbl 1230.82005 Wang, C.; Wise, S. M. 192 2011 An analysis of the total least squares problem. Zbl 0468.65011 Golub, Gene H.; Van Loan, Charles F. 192 1980 On the accuracy of the finite volume element method based on piecewise linear polynomials. Zbl 1036.65084 Ewing, Richard E.; Lin, Tao; Lin, Yanping 191 2002 Mixed finite elements for elliptic problems with tensor coefficients as cell-centered finite differences. Zbl 0880.65084 Arbogast, Todd; Wheeler, Mary F.; Yotov, Ivan 191 1997 Convergence of the mimetic finite difference method for diffusion problems on polyhedral meshes. Zbl 1108.65102 Brezzi, Franco; Lipnikov, Konstantin; Shashkov, Mikhail 190 2005 A family of fourth-order methods for nonlinear equations. Zbl 0266.65040 King, Richard F. 189 1973 Error estimates for a semidiscrete finite element method for fractional order parabolic equations. Zbl 1268.65126 Jin, Bangti; Lazarov, Raytcho; Zhou, Zhi 187 2013 Application of an ultra weak variational formulation of elliptic PDEs to the two-dimensional Helmholtz problem. Zbl 0955.65081 Cessenat, Olivier; Despres, Bruno 186 1998 A generalization of a theorem of Böcher. Zbl 0173.02703 Marden, M. 184 1966 Comparing numerical methods for ordinary differential equations. Zbl 0221.65115 Hull, T. E.; Enright, W. H.; Fellen, B. M.; Sedgwick, A. E. 181 1972 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. 181 1991 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 180 1997 Two-level method based on finite element and Crank-Nicolson extrapolation for the time-dependent Navier-Stokes equations. Zbl 1130.76365 He, Yinnian 179 2003 Explicit Runge-Kutta (-Nyström) methods with reduced phase errors for computing oscillating solutions. Zbl 0624.65058 Van der Houwen, P. J.; Sommeijer, B. P. 179 1987 Fundamental solutions method for elliptic boundary value problems. Zbl 0579.65121 Bogomolny, Alexander 178 1985 Superconvergence of the local discontinuous Galerkin method for elliptic problems on Cartesian grids. Zbl 1041.65080 Cockburn, Bernardo; Kanschat, Guido; Perugia, Ilaria; Schötzau, Dominik 177 2001 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 177 2007 Geometric two-scale integrators for highly oscillatory system: uniform accuracy and near conservations. Zbl 1517.65128 Wang, Bin; Zhao, Xiaofei 8 2023 Summation-by-parts operators for general function spaces. Zbl 07679126 Glaubitz, Jan; Nordström, Jan; Öffner, Philipp 5 2023 A new thermodynamically compatible finite volume scheme for magnetohydrodynamics. Zbl 07670867 Busto, Saray; Dumbser, Michael 5 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. 5 2023 A symmetrized parametric finite element method for anisotropic surface diffusion of closed curves. Zbl 1512.65205 Bao, Weizhu; Jiang, Wei; Li, Yifei 4 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 4 2023 Rank-adaptive time integration of tree tensor networks. Zbl 1511.65064 Ceruti, Gianluca; Lubich, Christian; Sulz, Dominik 4 2023 Analysis of error localization of Chebyshev spectral approximations. Zbl 1528.41016 Wang, Haiyong 4 2023 Direct guaranteed lower eigenvalue bounds with optimal a priori convergence rates for the bi-Laplacian. Zbl 1521.65118 Carstensen, Carsten; Puttkammer, Sophie 3 2023 A local discontinuous Galerkin approximation for the \(p\)-Navier-Stokes system. I: Convergence analysis. Zbl 1518.76035 Kaltenbach, Alex; RůžIčka, Michael 3 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 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. 2 2023 Efficient stability-preserving numerical methods for nonlinear coercive problems in vector space. Zbl 07679130 Wang, Wansheng; Li, Shoufu 2 2023 Optimization and convergence of numerical attractors for discrete-time quasi-linear lattice system. Zbl 1512.65161 Li, Yangrong; Yang, Shuang; Caraballo, Tomás 2 2023 An exponential spectral method using VP means for semilinear subdiffusion equations with rough data. Zbl 07754853 Li, Buyang; Lin, Yanping; Ma, Shu; Rao, Qiqi 2 2023 Wavenumber explicit convergence of a multiscale generalized finite element method for heterogeneous Helmholtz problems. Zbl 1517.65085 Chupeng, Ma; Alber, Christian; Scheichl, Robert 2 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 2 2023 An improved high-order method for elliptic multiscale problems. Zbl 07725052 Dong, Zhaonan; Hauck, Moritz; Maier, Roland 2 2023 Provably positive central discontinuous Galerkin schemes via geometric quasilinearization for ideal MHD equations. Zbl 1516.65102 Wu, Kailiang; Jiang, Haili; Shu, Chi-Wang 2 2023 Value-gradient based formulation of optimal control problem and machine learning algorithm. Zbl 1523.49031 Bensoussan, Alain; Han, Jiayue; Yam, Sheung Chi Phillip; Zhou, Xiang 2 2023 A unifying framework for interpolatory \(\mathcal{L}_2\)-optimal reduced-order modeling. Zbl 1523.30048 Mlinarić, Petar; Gugercin, Serkan 2 2023 A numerical energy reduction approach for semilinear diffusion-reaction boundary value problems based on steady-state iterations. Zbl 07679127 Amrein, Mario; Heid, Pascal; Wihler, Thomas P. 1 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. 1 2023 Convergence of a time discrete scheme for a chemotaxis-consumption model. Zbl 07764837 Guillén-González, Francisco; Corrêa Vianna Filho, André Luiz 1 2023 The unique continuation problem for the heat equation discretized with a high-order space-time nonconforming method. Zbl 07764838 Burman, Erik; Delay, Guillaume; Ern, Alexandre 1 2023 High-order BDF convolution quadrature for subdiffusion models with a singular source term. Zbl 07764839 Shi, Jiankang; Chen, Minghua 1 2023 Monte Carlo gradient in optimization constrained by radiative transport equation. Zbl 07770184 Li, Qin; Wang, Li; Yang, Yunan 1 2023 The mpEDMD algorithm for data-driven computations of measure-preserving dynamical systems. Zbl 1517.65038 Colbrook, Matthew J. 1 2023 On the convergence of discontinuous Galerkin/Hermite spectral methods for the Vlasov-Poisson system. Zbl 1519.65043 Bessemoulin-Chatard, Marianne; Filbet, Francis 1 2023 Gauge-transformed exponential integrator for generalized KdV equations with rough data. Zbl 07713540 Li, Bing; Wu, Yifei; Zhao, Xiaofei 1 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 1 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 07713544 Chaumont-Frelet, Théophile; Vohralík, Martin 1 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 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 Agglomeration-based geometric multigrid schemes for the virtual element method. Zbl 1512.65290 Antonietti, Paola F.; Berrone, Stefano; Busetto, Martina; Verani, Marco 1 2023 Convergence analysis of Newton-Schur method for symmetric elliptic eigenvalue problem. Zbl 1519.65051 Shao, Nian; Chen, Wenbin 1 2023 Adaptive finite element approximations for elliptic problems using regularized forcing data. Zbl 1515.65292 Heltai, Luca; Lei, Wenyu 1 2023 Computational lower bounds of the Maxwell eigenvalues. Zbl 1518.35581 Gallistl, Dietmar; Olkhovskiy, Vladislav 1 2023 Nonlinear eigenvalue methods for linear pointwise stability of nonlinear waves. Zbl 1510.65101 Scheel, Arnd 1 2023 Optimal analysis of non-uniform Galerkin-mixed finite element approximations to the Ginzburg-Landau equations in superconductivity. Zbl 1514.65128 Gao, Huadong; Sun, Weiwei 1 2023 Robust superlinear Krylov convergence for complex noncoercive compact-equivalent operator preconditioners. Zbl 1515.65073 Axelsson, Owe; Karátson, János; Magoulès, Frédéric 1 2023 Optimal \(L^2\) error estimates of unconditionally stable finite element schemes for the Cahn-Hilliard-Navier-Stokes system. Zbl 07688703 Cai, Wentao; Sun, Weiwei; Wang, Jilu; Yang, Zongze 1 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 1 2023 Generalized SAV-exponential integrator schemes for Allen-Cahn type gradient flows. Zbl 07572361 Ju, Lili; Li, Xiao; Qiao, Zhonghua 17 2022 A family of finite element Stokes complexes in three dimensions. Zbl 1522.65212 Hu, Kaibo; Zhang, Qian; Zhang, Zhimin 14 2022 Convergence analysis of the variational operator splitting scheme for a reaction-diffusion system with detailed balance. Zbl 07516278 Liu, Chun; Wang, Cheng; Wang, Yiwei; Wise, Steven M. 13 2022 Exponential convolution quadrature for nonlinear subdiffusion equations with nonsmooth initial data. Zbl 1496.65166 Li, Buyang; Ma, Shu 13 2022 Novel design and analysis of generalized finite element methods based on locally optimal spectral approximations. Zbl 07714591 Ma, Chupeng; Scheichl, Robert; Dodwell, Tim 12 2022 Improved uniform error bounds on time-splitting methods for long-time dynamics of the nonlinear Klein-Gordon equation with weak nonlinearity. Zbl 07572363 Bao, Weizhu; Cai, Yongyong; Feng, Yue 11 2022 Stability and error analysis of IMEX SAV schemes for the magneto-hydrodynamic equations. Zbl 1492.65269 Li, Xiaoli; Wang, Weilong; Shen, Jie 10 2022 A new Lagrange multiplier approach for constructing structure preserving schemes. II: Bound preserving. Zbl 1491.65110 Cheng, Qing; Shen, Jie 9 2022 Finite elements for div- and divdiv-conforming symmetric tensors in arbitrary dimension. Zbl 1496.65213 Chen, Long; Huang, Xuehai 8 2022 High order strong stability preserving multiderivative implicit and IMEX Runge-Kutta methods with asymptotic preserving properties. Zbl 1522.65120 Gottlieb, Sigal; Grant, Zachary J.; Hu, Jingwei; Shu, Ruiwen 7 2022 Local convergence of the FEM for the integral fractional Laplacian. Zbl 07534669 Faustmann, Markus; Karkulik, Michael; Melenk, Jens Markus 6 2022 Convergence of renormalized finite element methods for heat flow of harmonic maps. Zbl 07714593 Gui, Xinping; Li, Buyang; Wang, Jilu 6 2022 Computing semigroups with error control. Zbl 1520.65033 Colbrook, Matthew J. 6 2022 Temporal second-order finite difference schemes for variable-order time-fractional wave equations. Zbl 1481.65128 Du, Rui-lian; Sun, Zhi-zhong; Wang, Hong 6 2022 Stability of variable-step BDF2 and BDF3 methods. Zbl 1501.65041 Li, Zhaoyi; Liao, Hong-lin 6 2022 A variable time step time filter algorithm for the geothermal system. Zbl 1505.76061 Qin, Yi; Wang, Yongshuai; Li, Jian 6 2022 Error estimates for Euler discretization of high-index saddle dynamics. Zbl 1507.37110 Zhang, Lei; Zhang, Pingwen; Zheng, Xiangcheng 6 2022 \(H^m\)-conforming virtual elements in arbitrary dimension. Zbl 1514.65166 Chen, Chunyu; Huang, Xuehai; Wei, Huayi 6 2022 Locking-free enriched Galerkin method for linear elasticity. Zbl 1483.65195 Yi, Son-Young; Lee, Sanghyun; Zikatanov, Ludmil 5 2022 Hybrid high-order and weak Galerkin methods for the biharmonic problem. Zbl 1501.65111 Dong, Zhaonan; Ern, Alexandre 5 2022 Stratified radiative transfer in a fluid and numerical applications to Earth science. Zbl 1502.35173 Golse, François; Pironneau, Olivier R. 5 2022 Moment preserving Fourier-Galerkin spectral methods and application to the Boltzmann equation. Zbl 1511.76073 Pareschi, Lorenzo; Rey, Thomas 5 2022 On the convergence of adaptive stochastic collocation for elliptic partial differential equations with affine diffusion. Zbl 1508.65163 Eigel, Martin; Ernst, Oliver G.; Sprungk, Björn; Tamellini, Lorenzo 5 2022 A note on sampling recovery of multivariate functions in the uniform norm. Zbl 1510.94078 Pozharska, Kateryna; Ullrich, Tino 5 2022 MINRES for second-order PDEs with singular data. Zbl 1491.65136 Führer, Thomas; Heuer, Norbert; Karkulik, Michael 4 2022 Flux-mortar mixed finite element methods on nonmatching grids. Zbl 1493.65192 Boon, Wietse M.; Gläser, Dennis; Helmig, Rainer; Yotov, Ivan 4 2022 A unified convergence analysis for the fractional diffusion equation driven by fractional Gaussian noise with Hurst index \(H\in(0,1)\). Zbl 07556062 Nie, Daxin; Deng, Weihua 4 2022 A \(C^1\) conforming Petrov-Galerkin method for convection-diffusion equations and superconvergence analysis over rectangular meshes. Zbl 07714592 Cao, Waixiang; Jia, Lueling; Zhang, Zhimin 4 2022 Fractional semilinear optimal control: optimality conditions, convergence, and error analysis. Zbl 1527.49026 Otárola, Enrique 4 2022 Isoparametric unfitted BDF-finite element method for PDEs on evolving domains. Zbl 1501.65076 Lou, Yimin; Lehrenfeld, Christoph 4 2022 Sinc-\(\theta\) schemes for backward stochastic differential equations. Zbl 1506.65024 Wang, Xu; Zhao, Weidong; Zhou, Tao 4 2022 Sharper error estimates for virtual elements and a bubble-enriched version. Zbl 1498.65195 Beirão da Veiga, L.; Vacca, G. 4 2022 Uniformly accurate low regularity integrators for the Klein-Gordon equation from the classical to nonrelativistic limit regime. Zbl 1492.35297 Calvo, María Cabrera; Schratz, Katharina 3 2022 An embedded exponential-type low-regularity integrator for mKdV equation. Zbl 07534667 Ning, Cui; Wu, Yifei; Zhao, Xiaofei 3 2022 Optimal maximum norm estimates for virtual element methods. Zbl 1491.65139 He, Wen-Ming; Guo, Hailong 3 2022 Analysis and approximations of Dirichlet boundary control of Stokes flows in the energy space. Zbl 1518.49002 Gong, Wei; Mateos, Mariano; Singler, John; Zhang, Yangwen 3 2022 On the stability of unconditionally positive and linear invariants preserving time integration schemes. Zbl 1506.65098 Izgin, Thomas; Kopecz, Stefan; Meister, Andreas 3 2022 The discovery of dynamics via linear multistep methods and deep learning: error estimation. Zbl 1506.65105 Du, Qiang; Gu, Yiqi; Yang, Haizhao; Zhou, Chao 3 2022 On the coupling of the curved virtual element method with the one-equation boundary element method for 2D exterior Helmholtz problems. Zbl 1501.65145 Desiderio, Luca; Falletta, Silvia; Ferrari, Matteo; Scuderi, Letizia 3 2022 Convergence analysis of a fully discrete energy-stable numerical scheme for the Q-tensor flow of liquid crystals. Zbl 1508.65102 Gudibanda, Varun M.; Weber, Franziska; Yue, Yukun 3 2022 A fourth-order unfitted characteristic finite element method for solving the advection-diffusion equation on time-varying domains. Zbl 1503.65240 Ma, Chuwen; Zhang, Qinghai; Zheng, Weiying 3 2022 A semi-implicit exponential low-regularity integrator for the Navier-Stokes equations. Zbl 1503.65237 Li, Buyang; Ma, Shu; Schratz, Katharina 3 2022 Optimized transmission conditions in domain decomposition methods with cross-points for Helmholtz equation. Zbl 1505.65304 Després, B.; Nicolopoulos, A.; Thierry, B. 3 2022 Convergence analysis of discrete high-index saddle dynamics. Zbl 1506.37101 Luo, Yue; Zheng, Xiangcheng; Cheng, Xiangle; Zhang, Lei 3 2022 Identification of potential in diffusion equations from terminal observation: analysis and discrete approximation. Zbl 1506.65144 Zhang, Zhengqi; Zhang, Zhidong; Zhou, Zhi 3 2022 Full discretization of Cauchy’s problem by Lavrentiev-finite element method. Zbl 07498293 Ben Belgacem, Faker; Girault, Vivette; Jelassi, Faten 3 2022 Well-posedness and convergence of a finite volume method for conservation laws on networks. Zbl 07498295 Fjordholm, Ulrik S.; Musch, Markus; Risebro, Nils H. 3 2022 Neural parametric Fokker-Planck equation. Zbl 1493.65132 Liu, Shu; Li, Wuchen; Zha, Hongyuan; Zhou, Haomin 3 2022 Coupling parareal with optimized Schwarz waveform relaxation for parabolic problems. Zbl 1492.65260 Bui, Duc Quang; Japhet, Caroline; Maday, Yvon; Omnes, Pascal 2 2022 Conforming finite element divdiv complexes and the application for the linearized Einstein-Bianchi system. Zbl 1490.65275 Hu, Jun; Liang, Yizhou; Ma, Rui 2 2022 A well-posed first order system least squares formulation of the instationary Stokes equations. Zbl 07556064 Gantner, Gregor; Stevenson, Rob 2 2022 On maximal regularity estimates for discontinuous Galerkin time-discrete methods. Zbl 07714588 Akrivis, Georgios; Makridakis, Charalambos 2 2022 Accuracy of spectral element method for wave, parabolic, and Schrödinger equations. Zbl 1525.65094 Li, Hao; Appelö, Daniel; Zhang, Xiangxiong 2 2022 Convergence analysis of inexact two-grid methods: a theoretical framework. Zbl 1481.65049 Xu, Xuefeng; Zhang, Chen-Song 2 2022 A monotone discretization for integral fractional Laplacian on bounded Lipschitz domains: pointwise error estimates under Hölder regularity. Zbl 1506.65184 Han, Rubing; Wu, Shuonan 2 2022 On convergence of numerical solutions for the compressible MHD system with exactly divergence-free magnetic field. Zbl 1513.76173 Li, Yang; She, Bangwei 2 2022 On energy laws and stability of Runge-Kutta methods for linear seminegative problems. Zbl 1502.65143 Sun, Zheng; Wei, Yuanzhe; Wu, Kailiang 2 2022 ...and 1722 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 53,855 Authors 222 Shu, Chi-Wang 219 Dehghan Takht Fooladi, Mehdi 194 He, Yinnian 160 Chen, Yanping 157 Argyros, Ioannis Konstantinos 157 Huang, Yunqing 153 Zhang, Zhimin 146 Shi, Dongyang 143 Carstensen, Carsten 140 Schwab, Christoph 132 Wang, Hong 117 Rui, Hongxing 115 Burman, Erik 115 Liu, Fawang 113 Gatica, Gabriel N. 112 Feng, Xinlong 110 Gunzburger, Max D. 107 Cockburn, Bernardo 107 Simos, Theodore E. 106 Zhang, Shangyou 102 Du, Qiang 102 Wheeler, Mary Fanett 101 Chung, Tsz Shun Eric 101 Shen, Jie 101 Yang, Xiaofeng 100 Dumbser, Michael 100 Gander, Martin Jakob 100 Quarteroni, Alfio M. 98 Beirão da Veiga, Lourenço 95 Babuška, Ivo 95 Ern, Alexandre 95 Nochetto, Ricardo Horacio 94 Jackiewicz, Zdzislaw 91 Karniadakis, George Em 91 Xu, Da 90 Evans, David John 90 Ye, Xiu 88 Hou, Yanren 88 Li, Jichun 88 Wei, Yimin 87 Brenner, Susanne Cecelia 86 Praetorius, Dirk 86 Wohlmuth, Barbara I. 86 Xu, Jinchao 85 Huang, Chengming 84 Huang, Ting-Zhu 84 Hughes, Thomas J. 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