| # | Title | Journal | Year | Citations |
|---|
| 1 | On the Construction and Comparison of Difference Schemes | SIAM Journal on Numerical Analysis | 1968 | 2,767 |
| 2 | Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems | SIAM Journal on Numerical Analysis | 2002 | 2,483 |
| 3 | High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws | SIAM Journal on Numerical Analysis | 1984 | 2,214 |
| 4 | The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems | SIAM Journal on Numerical Analysis | 1998 | 1,854 |
| 5 | Monotone Piecewise Cubic Interpolation | SIAM Journal on Numerical Analysis | 1980 | 1,750 |
| 6 | An Analysis of the Total Least Squares Problem | SIAM Journal on Numerical Analysis | 1980 | 1,533 |
| 7 | Iterative Solution of Implicit Approximations of Multidimensional Partial Differential Equations | SIAM Journal on Numerical Analysis | 1968 | 1,521 |
| 8 | Image Selective Smoothing and Edge Detection by Nonlinear Diffusion. II | SIAM Journal on Numerical Analysis | 1992 | 1,377 |
| 9 | Image Selective Smoothing and Edge Detection by Nonlinear Diffusion | SIAM Journal on Numerical Analysis | 1992 | 1,346 |
| 10 | Splitting Algorithms for the Sum of Two Nonlinear Operators | SIAM Journal on Numerical Analysis | 1979 | 1,326 |
| 11 | Inexact Newton Methods | SIAM Journal on Numerical Analysis | 1982 | 1,290 |
| 12 | Solution of Sparse Indefinite Systems of Linear Equations | SIAM Journal on Numerical Analysis | 1975 | 1,271 |
| 13 | Error Estimates for Adaptive Finite Element Computations | SIAM Journal on Numerical Analysis | 1978 | 1,212 |
| 14 | The Differentiation of Pseudo-Inverses and Nonlinear Least Squares Problems Whose Variables Separate | SIAM Journal on Numerical Analysis | 1973 | 1,190 |
| 15 | An Interior Penalty Finite Element Method with Discontinuous Elements | SIAM Journal on Numerical Analysis | 1982 | 1,190 |
| 16 | The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources | SIAM Journal on Numerical Analysis | 1994 | 1,113 |
| 17 | A Convergent Adaptive Algorithm for Poisson’s Equation | SIAM Journal on Numerical Analysis | 1996 | 974 |
| 18 | Numerical Methods for Convection-Dominated Diffusion Problems Based on Combining the Method of Characteristics with Finite Element or Finite Difference Procedures | SIAM Journal on Numerical Analysis | 1982 | 923 |
| 19 | A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data | SIAM Journal on Numerical Analysis | 2007 | 922 |
| 20 | A Nonmonotone Line Search Technique for Newton’s Method | SIAM Journal on Numerical Analysis | 1986 | 910 |
| 21 | A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods | SIAM Journal on Numerical Analysis | 2002 | 902 |
| 22 | An Algorithm for Generalized Matrix Eigenvalue Problems | SIAM Journal on Numerical Analysis | 1973 | 896 |
| 23 | Nested Dissection of a Regular Finite Element Mesh | SIAM Journal on Numerical Analysis | 1973 | 845 |
| 24 | On Godunov-Type Methods for Gas Dynamics | SIAM Journal on Numerical Analysis | 1988 | 831 |
| 25 | Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems | SIAM Journal on Numerical Analysis | 2009 | 830 |
| 26 | A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data | SIAM Journal on Numerical Analysis | 2008 | 819 |
| 27 | Uniformly High-Order Accurate Nonoscillatory Schemes. I | SIAM Journal on Numerical Analysis | 1987 | 757 |
| 28 | Variational Iterative Methods for Nonsymmetric Systems of Linear Equations | SIAM Journal on Numerical Analysis | 1983 | 745 |
| 29 | Implicit-Explicit Methods for Time-Dependent Partial Differential Equations | SIAM Journal on Numerical Analysis | 1995 | 741 |
| 30 | The Rotation of Eigenvectors by a Perturbation. III | SIAM Journal on Numerical Analysis | 1970 | 740 |
| 31 | Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations | SIAM Journal on Numerical Analysis | 2004 | 707 |
| 32 | Feature-Oriented Image Enhancement Using Shock Filters | SIAM Journal on Numerical Analysis | 1990 | 692 |
| 33 | Finite Element Approximation of the Nonstationary Navier–Stokes Problem. I. Regularity of Solutions and Second-Order Error Estimates for Spatial Discretization | SIAM Journal on Numerical Analysis | 1982 | 690 |
| 34 | A Globally Convergent Augmented Lagrangian Algorithm for Optimization with General Constraints and Simple Bounds | SIAM Journal on Numerical Analysis | 1991 | 666 |
| 35 | Practical Approximate Solutions to Linear Operator Equations When the Data are Noisy | SIAM Journal on Numerical Analysis | 1977 | 665 |
| 36 | Finite-Element Approximation of the Nonstationary Navier–Stokes Problem. Part IV: Error Analysis for Second-Order Time Discretization | SIAM Journal on Numerical Analysis | 1990 | 664 |
| 37 | On Direct Methods for Solving Poisson’s Equations | SIAM Journal on Numerical Analysis | 1970 | 657 |
| 38 | The Conjugate Gradient Method and Trust Regions in Large Scale Optimization | SIAM Journal on Numerical Analysis | 1983 | 640 |
| 39 | On the $O(1/n)$ Convergence Rate of the Douglas–Rachford Alternating Direction Method | SIAM Journal on Numerical Analysis | 2012 | 623 |
| 40 | An Elliptic Collocation-Finite Element Method with Interior Penalties | SIAM Journal on Numerical Analysis | 1978 | 619 |
| 41 | High-Order Essentially Nonoscillatory Schemes for Hamilton–Jacobi Equations | SIAM Journal on Numerical Analysis | 1991 | 615 |
| 42 | On Krylov Subspace Approximations to the Matrix Exponential Operator | SIAM Journal on Numerical Analysis | 1997 | 613 |
| 43 | On a Class of High Resolution Total-Variation-Stable Finite-Difference Schemes | SIAM Journal on Numerical Analysis | 1984 | 606 |
| 44 | High-Resolution Conservative Algorithms for Advection in Incompressible Flow | SIAM Journal on Numerical Analysis | 1996 | 580 |
| 45 | Two-Grid Discretization Techniques for Linear and Nonlinear PDEs | SIAM Journal on Numerical Analysis | 1996 | 577 |
| 46 | Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation | SIAM Journal on Numerical Analysis | 2017 | 577 |
| 47 | Stability Theory for Systems of Inequalities, Part II: Differentiable Nonlinear Systems | SIAM Journal on Numerical Analysis | 1976 | 575 |
| 48 | A Priori $L_2 $ Error Estimates for Galerkin Approximations to Parabolic Partial Differential Equations | SIAM Journal on Numerical Analysis | 1973 | 574 |
| 49 | Error Estimate Procedure in the Finite Element Method and Applications | SIAM Journal on Numerical Analysis | 1983 | 570 |
| 50 | A Well-Balanced Scheme for the Numerical Processing of Source Terms in Hyperbolic Equations | SIAM Journal on Numerical Analysis | 1996 | 562 |
