A note onp/hp finite element methods for reaction-diffusion problems in polygonal domains

DOI<391::AID-CNM342>3.0.CO;2-0 10.1002/1099-0887(200006)16:6<391::AID-CNM342>3.0.CO;2-0zbMath0958.65101OpenAlexW2042853796MaRDI QIDQ4495458

Christos Xenophontos

Publication date: 10 April 2001

Full work available at URL: https://doi.org/10.1002/1099-0887(200006)16:6<391::aid-cnm342>3.0.co;2-0

zbMATH Keywords

numerical examplesreaction-diffusion problemscorner singularitiesboundary layersmesh generation\(p/hp\) finite element methods

Mathematics Subject Classification ID

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) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

Cites Work

• The h-p version of the finite element method. I. The basic approximation results
• The \(hp\) finite element method for problems in mechanics with boundary layers
• Differentiability Properties of Solutions of the Equation $ - \varepsilon ^2 \Delta u + ru = f(x,y)$ in a Square
• The Optimal Convergence Rate of the p-Version of the Finite Element Method
• hp FEM for Reaction-Diffusion Equations I: Robust Exponential Convergence
• Finite element computations for the Reissner-Mindlin plate model
• Thehp finite element method for singularly perturbed problems in nonsmooth domains
• THE hp FINITE ELEMENT METHOD FOR SINGULARLY PERTURBED PROBLEMS IN SMOOTH DOMAINS
• The $p$ and $hp$ versions of the finite element method for problems with boundary layers

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