Uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems: convection—diffusion type

[1]  Christos Xenophontos,et al.  The hp finite element method for problems in mechanics with boundary layers , 1998 .

[2]  I. M. Navon,et al.  Uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems I: Reaction-diffusion Type , 1998, Computers & Mathematics with Applications.

[3]  R. Bruce Kellogg,et al.  Optimal Approximability of Solutions of Singularly Perturbed Two-Point Boundary Value Problems , 1997 .

[4]  Jichun Li,et al.  Quasioptimal uniformly convergent finite element methods for the elliptic boundary layer problem , 1997 .

[5]  Martin Stynes,et al.  EFFICIENT GENERATION OF ORIENTED MESHES FOR SOLVING CONVECTION-DIFFUSION PROBLEMS , 1997 .

[6]  Christoph Schwab,et al.  The p and hp versions of the finite element method for problems with boundary layers , 1996, Math. Comput..

[7]  HANS-GäRG Roos,et al.  A note on the conditioning of upwind schemes on Shishkin meshes , 1996 .

[8]  Thomas J. R. Hughes,et al.  Stabilization Techniques and Subgrid Scales Capturing , 1996 .

[9]  J. Cole,et al.  Multiple Scale and Singular Perturbation Methods , 1996 .

[10]  Joseph E. Flaherty,et al.  High-Order Finite Element Methods for Singularly Perturbed Elliptic and Parabolic Problems , 1995, SIAM J. Appl. Math..

[11]  Eugene O'Riordan,et al.  Special meshes for finite difference approximations to an advection-diffusion equation with parabolic layers , 1995 .

[12]  T. A. Manteuffel,et al.  Accurate discretization for singular perturbations: the one-dimensional case , 1995 .

[13]  C. Farhat,et al.  Bubble Functions Prompt Unusual Stabilized Finite Element Methods , 1994 .

[14]  Wu Qi-guang,et al.  Numerical solutions for singularly perturbed semi-linear parabolic equation , 1993 .

[15]  R. Bank,et al.  The hierarchical basis multigrid method for convection-diffusion equations , 1992 .

[16]  M. Stynes,et al.  A globally uniformly convergent finite element method for a singularly perturbed elliptic problem in two dimensions , 1991 .

[17]  Youcef Saad,et al.  A Basic Tool Kit for Sparse Matrix Computations , 1990 .

[18]  Shagi-Di Shih,et al.  Asymptotic anaylsis of a singular perturbation problem , 1987 .

[19]  A. H. Schatz,et al.  Crosswind Smear and Pointwise Errors in Streamline Diffusion Finite Element Methods , 1987 .

[20]  Leszek Demkowicz,et al.  An adaptive characteristic Petrov-Galerkin finite element method for convection-dominated linear and nonlinear parabolic problems in one space variable , 1986 .

[21]  J. Oden,et al.  Finite Elements: Mathematical Aspects (Volume IV) , 1986 .

[22]  Claes Johnson,et al.  Finite element methods for linear hyperbolic problems , 1984 .

[23]  W. Eckhaus.  Asymptotic Analysis of Singular Perturbations , 1979 .

[24]  G. Strang,et al.  An Analysis of the Finite Element Method , 1974 .

[25]  Rolf Rannacher,et al.  Pointwise superconvergence of the streamline diffusion finite-element method , 1996 .

[26]  Lutz Tobiska,et al.  Numerical Methods for Singularly Perturbed Differential Equations , 1996 .

[27]  Leonid V. Kalachev,et al.  The Boundary Function Method for Singular Perturbation Problems , 1995 .

[28]  Martin Stynes,et al.  Pointwise Error Estimates for a Streamline Diffusion Scheme on a Shishkin Mesh for a Convection-Diff , 1995 .

[29]  Paul A. Farrell,et al.  Discrete approximations for singularly perturbed boundary value problems with parabolic layers , 1995 .

[30]  M. Stynes,et al.  Necessary Conditions for Uniform Convergence of Nite Diierence Schemes for Convection-diiusion Problems with Exponential and Parabolic Layers , 1995 .

[31]  M. Stynes,et al.  Finite-element methods for singularly perturbed high-order elliptic two-point boundary value problems. II: convection-diffusion-type problems , 1995 .

[32]  L. R. Scott,et al.  The Mathematical Theory of Finite Element Methods , 1994 .

[33]  J. R. E. O’Malley.  Singular perturbation methods for ordinary differential equations , 1991 .

[34]  J. Tinsley Oden,et al.  Finite Elements: Fluid Mechanics. , 1989 .

[35]  G. I. SHISHKIN,et al.  Grid approximation of singularly perturbed parabolic equations with internal layers , 1988 .

[36]  Wil H. A. Schilders,et al.  Uniform Numerical Methods for Problems with Initial and Boundary Layers , 1980 .

[37]  J. Z. Zhu,et al.  The finite element method , 1977 .

[38]  O. C. Zienkiewicz,et al.  Quadratic finite element schemes for two-dimensional convective-transport problems , 1977 .