Thehp finite element method for singularly perturbed problems in nonsmooth domains

DOI<63::AID-NUM4>3.0.CO;2-T 10.1002/(SICI)1098-2426(199901)15:1<63::AID-NUM4>3.0.CO;2-TzbMath0930.65126OpenAlexW1967328313MaRDI QIDQ4256033

Christos Xenophontos

Publication date: 28 June 1999

Full work available at URL: https://doi.org/10.1002/(sici)1098-2426(199901)15:1<63::aid-num4>3.0.co;2-t

zbMATH Keywords

singular perturbationboundary layercorner layerselliptic boundary value problems\(hp\) finite element method

Mathematics Subject Classification ID

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

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Cites Work

• The h-p version of the finite element method. I. The basic approximation results
• The h, p and h-p versions of the finite element method in 1 dimension. I. The error analysis of the p-version
• 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
• Regularity of the Solution of Elliptic Problems with Piecewise Analytic Data. Part I. Boundary Value Problems for Linear Elliptic Equation of Second Order
• 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