An adaptive discontinuous finite volume method for elliptic problems

DOI10.1016/j.cam.2011.05.051zbMath1227.65101OpenAlexW1979656672WikidataQ62727813 ScholiaQ62727813MaRDI QIDQ719428

Jiangguo Liu, Lin Mu, Xiu Ye

Publication date: 10 October 2011

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

Full work available at URL: https://doi.org/10.1016/j.cam.2011.05.051

zbMATH Keywords

convergencenumerical experimentsLaplace equationa posteriori error estimatorhomogeneous Dirichlet boundary value problemadaptive mesh refinementsdiscontinuous finite volume method

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Finite volume methods for boundary value problems involving PDEs (65N08)

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Uses Software

• AFEM@matlab

Cites Work

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• A posteriori error control for a weakly over-penalized symmetric interior penalty method
• A posteriorierror analysis of a cell-centered finite volume method for semilinear elliptic problems
• A weakly over-penalized symmetric interior penalty method
• A posteriori error estimation and adaptive mesh-refinement techniques
• Adaptive finite element methods with convergence rates
• A posterior error estimate for finite volume methods of the second order elliptic problem
• A Note on Constant-Free A Posteriori Error Estimates
• Real Interpolation of Sobolev Spaces on Subdomains of Rn
• A New Discontinuous Finite Volume Method for Elliptic Problems
• Convergence of Adaptive Finite Element Methods
• Convergence Analysis of an Adaptive Interior Penalty Discontinuous Galerkin Method
• Convergence of Adaptive Discontinuous Galerkin Approximations of Second‐Order Elliptic Problems
• The Mathematical Theory of Finite Element Methods

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