Robust exponential convergence of \(hp\)-FEM in balanced norms for singularly perturbed reaction-diffusion equations

DOI10.1007/s10092-015-0139-yzbMath1336.65148arXiv1408.3328OpenAlexW2061478941MaRDI QIDQ260144

Jens Markus Melenk, Christos Xenophontos

Publication date: 18 March 2016

Published in: Calcolo (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.3328

zbMATH Keywords

singular perturbationfinite element methodboundary layersreaction-diffusion equationexponential convergencebalanced norm

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (19)

A \(C^{1}\)-conforming \(hp\) finite element method for fourth order singularly perturbed boundary value problems ⋮ An \(hp\) finite element method for \(4^{\mathrm{th}}\) order singularly perturbed problems ⋮ Robust exponential convergence of \(hp\)-FEM in balanced norms for singularly perturbed reaction-diffusion problems: corner domains ⋮ Robust coupling of DPG and BEM for a singularly perturbed transmission problem ⋮ A Robust DPG Method for Singularly Perturbed Reaction-Diffusion Problems ⋮ Exponential convergence of \textit{hp} FEM for spectral fractional diffusion in polygons ⋮ Mixed hp finite element method for singularly perturbed fourth order boundary value problems with two small parameters ⋮ Robust estimates in balanced norms for singularly perturbed reaction diffusion equations using graded meshes ⋮ Exponential Convergence of a Generalized FEM for Heterogeneous Reaction-Diffusion Equations ⋮ Finite element approximation of reaction-diffusion problems using an exponentially graded mesh ⋮ Isogeometric analysis for singularly perturbed high-order, two-point boundary value problems of reaction-diffusion type ⋮ First-Order System Least Squares Finite-Elements for Singularly Perturbed Reaction-Diffusion Equations ⋮ On the local discontinuous Galerkin method for singularly perturbed problem with two parameters ⋮ A weighted and balanced FEM for singularly perturbed reaction-diffusion problems ⋮ A mixed hp FEM for the approximation of fourth‐order singularly perturbed problems on smooth domains ⋮ Isogeometric analysis for singularly perturbed problems in 1-D: error estimates ⋮ Low-rank tensor approximation of singularly perturbed boundary value problems in one dimension ⋮ Balanced-norm error estimate of the local discontinuous Galerkin method on layer-adapted meshes for reaction-diffusion problems ⋮ Optimal order uniform convergence in energy and balanced norms of weak Galerkin finite element method on Bakhvalov-type meshes for nonlinear singularly perturbed problems

Cites Work

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• Analytic regularity for a singularly perturbed system of reaction-diffusion equations with multiple scales
• \(hp\)-finite element methods for singular perturbations
• Error estimation in a balanced norm for a convection-diffusion problem with two different boundary layers
• Convergence and stability in balanced norms of finite element methods on Shishkin meshes for reaction‐diffusion problems
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• hp FEM for Reaction-Diffusion Equations I: Robust Exponential Convergence
• On the robust exponential convergence of hp finite element methods for problems with boundary layers
• The $p$ and $hp$ versions of the finite element method for problems with boundary layers
• A Balanced Finite Element Method for Singularly Perturbed Reaction-Diffusion Problems
• Robust exponential convergence of hp FEM for singularly perturbed reaction-diffusion systems with multiple scales

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