High Order Continuous Local-Conserving Fluxes and Finite-Volume-Like Finite Element Solutions for Elliptic Equations

DOI10.1137/16M1066567zbMath1377.65154OpenAlexW2767260207MaRDI QIDQ4591220

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Publication date: 13 November 2017

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/16m1066567

zbMATH Keywords

fluxconvergencefinite element methodfinite volumenumerical experimentpostprocessinghigh orderlocal conservation

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items (10)

A new high order finite volume element solution on arbitrary triangular and quadrilateral meshes ⋮ Three dimensional high order finite volume element schemes for elliptic equations ⋮ A Finite Volume Element Solution Based on Postprocessing Technique Over Arbitrary Convex Polygonal Meshes ⋮ A polygonal finite volume element method for anisotropic diffusion problems ⋮ Unnamed Item ⋮ A unified analysis of a class of quadratic finite volume element schemes on triangular meshes ⋮ High order locally conservative finite element solutions for anisotropic diffusion problems in two dimensions ⋮ Construction of locally conservative fluxes for high order continuous Galerkin finite element methods ⋮ A Conservative Flux Optimization Finite Element Method for Convection-diffusion Equations ⋮ Unnamed Item

Cites Work

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• Development and analysis of higher order finite volume methods over rectangles for elliptic equations
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• High-order well-balanced finite volume WENO schemes for shallow water equation with moving water
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• A Locally Conservative Finite Element Method Based on Piecewise Constant Enrichment of the Continuous Galerkin Method
• Some Error Estimates for the Box Method
• Why Nonconservative Schemes Converge to Wrong Solutions: Error Analysis
• ConservativeP1 Conforming and Nonconforming Galerkin FEMs: Effective Flux Evaluation via a Nonmixed Method Approach
• Finite Volume Methods for Hyperbolic Problems
• On the Construction and Analysis of High Order Locally Conservative Finite Volume-Type Methods for One-Dimensional Elliptic Problems
• Local Mass-Corrections for Continuous Pressure Approximations of Incompressible Flow
• On the Application of the Continuous Galerkin Finite Element Method for Conservation Problems
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