Convergence analysis of finite element methods for singularly perturbed problems
DOI10.1016/S0898-1221(00)00192-9zbMath0961.65069MaRDI QIDQ1591920
Publication date: 14 January 2001
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
convergenceGalerkin methodsingular perturbationerror estimatesfinite element methodsboundary layerShiskin-meshes
Stability and convergence of numerical methods for ordinary differential equations (65L20) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Linear boundary value problems for ordinary differential equations (34B05) Singular perturbations for ordinary differential equations (34E15) Numerical solution of ill-posed problems involving ordinary differential equations (65L08)
Related Items
Cites Work
- Full-order convergence of a mixed finite element method for fourth-order elliptic equations
- Anisotropic mesh refinement for a singularly perturbed reaction diffusion model problem
- Numerical solutions for singularly perturbed semi-linear parabolic equation
- The full approximation accuracy for the stream function-vorticity- pressure method
- Quasioptimal uniformly convergent finite element methods for the elliptic boundary layer problem
- An almost fourth order uniformly convergent difference scheme for a semilinear singularly perturbed reaction-diffusion problem
- Global uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems: Higher-order elements
- Numerical solution of a quasilinear parabolic equation with a boundary layer
- On piecewise-uniform meshes for upwind- and central-difference operators for solving singularly perturbed problems
- Finite-element methods for singularly perturbed high-order elliptic two-point boundary value problems. I: reaction-diffusion-type problems
- Heterogeneous Domain Decomposition for Singularly Perturbed Elliptic Boundary Value Problems
- Layer-Adapted Grids for Singular Perturbation Problems
- Uniform Convergence and Superconvergence of Mixed Finite Element Methods on Anisotropically Refined Grids
- A Priori $L_2 $ Error Estimates for Galerkin Approximations to Parabolic Partial Differential Equations
- Convergence and superconvergence analysis of finite element methods on highly nonuniform anisotropic meshes for singularly perturbed reaction-diffusion problems
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item