Penalty combinations of the Ritz-Galerkin and finite difference methods for singularity problems

DOI10.1016/S0377-0427(96)00148-3zbMath0886.65106MaRDI QIDQ1362344

O. Diekmann

Publication date: 20 April 1998

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

finite element methodnumerical experimentserror boundspenalty methodRitz-Galerkin methodprojective methodsdifference methodssingular functionscombined methods

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (10)

Superconvergence of solution derivatives for the Shortley--Weller difference approximation of Poisson's equation. I: Smoothness problems ⋮ Global superconvergence of finite element methods for biharmonic equations and blending surfaces ⋮ The solution of Laplacian problems over L-shaped domains with a singular function boundary integral method ⋮ Particular solutions of singularly perturbed partial differential equations with constant coefficients in rectangular domains. I: Convergence analysis. ⋮ Interior boundary conditions in the Schwarz alternating method for the Trefftz method ⋮ Superconvergence of coupling techniques in combined methods for elliptic equations with singularities ⋮ Superconvergence of Solution Derivatives for the Shortley–Weller Difference Approximation for Parabolic Problems ⋮ Global superconvergence in combinations of Ritz-Galerkin-FEM for singularity problems ⋮ The finite volume method and application in combinations ⋮ Singularities and treatments of elliptic boundary value problems.

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Superconvergence phenomenon in the finite element method arising from averaging gradients
• On a global superconvergence of the gradient of linear triangular elements
• Superconvergence analysis of approximate boundary-flux calculations
• The Finite Volume Element Method for Diffusion Equations on General Triangulations
• Nodal Superconvergence and Solution Enhancement for a Class of Finite-Element and Finite-Difference Methods
• On the Accuracy of the Finite Volume Element Method for Diffusion Equations on Composite Grids
• Penalty-combined approaches to the Ritz-Galerkin and finite element methods for singularity problems of elliptic equations
• An approach combining the Ritz‐Galerkin and finite difference methods
• Superconvergent recovery of gradients on subdomains from piecewise linear finite‐element approximations
• Superconvergence of the gradient of Galerkin approximations for elliptic problems

This page was built for publication: Penalty combinations of the Ritz-Galerkin and finite difference methods for singularity problems