A novel nonconforming uniformly convergent finite element method in two dimensions

DOI10.1006/jmaa.1996.0283zbMath0859.65118OpenAlexW2079854659MaRDI QIDQ1922960

Dirk Adam, Andreas Felgenhauer, Hans-Goerg Roos

Publication date: 15 April 1997

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.1996.0283

zbMATH Keywords

singular perturbationuniform convergenceboundary layersnonconforming Galerkin finite element method

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

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Novel fitted operator finite difference methods for singularly perturbed elliptic convection–diffusion problems in two dimensions ⋮ A uniformly convergent Galerkin method on a Shishkin mesh for a convection-diffusion problem ⋮ A priori estimates for the solution of convection-diffusion problems and interpolation on Shishkin meshes ⋮ A robust finite element method for a singularly perturbed elliptic problem with two small parameters ⋮ A global uniformly convergent finite element method for a quasi-linear singularly perturbed elliptic problem ⋮ MULTISCALE NUMERICAL METHODS FOR SINGULARLY PERTURBED CONVECTION-DIFFUSION EQUATIONS ⋮ Global uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems: Higher-order elements ⋮ A nonconforming combination of the finite element and volume methods with an anisotropic mesh refinement for a singularly perturbed convection-diffusion equation ⋮ An arbitrary order uniformly convergent finite element method for singular perturbation problems ⋮ An analysis of a conforming exponentially fitted finite element method for a convection-diffusion problem

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