On the Construction and Analysis of Finite Volume Element Schemes with Optimal $L^2$ Convergence Rate

DOI10.4208/nmtma.OA-2020-0027zbMath1488.65204OpenAlexW3106800185MaRDI QIDQ5153431

Xiang Wang, Yu Qing Zhang

Publication date: 29 September 2021

Published in: Numerical Mathematics: Theory, Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4208/nmtma.oa-2020-0027

zbMATH Keywords

finite volumesufficient and necessary conditionorthogonal condition\({L^2}\) estimate

Mathematics Subject Classification ID

Diffusion (76R50) Stability and convergence of numerical methods for ordinary differential equations (65L20) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10)

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A fast matrix-free approach to the high-order control volume finite element method with application to low-Mach flow ⋮ A Quadratic Serendipity Finite Volume Element Method on Arbitrary Convex Polygonal Meshes ⋮ Three dimensional high order finite volume element schemes for elliptic equations ⋮ New Superconvergent Structures with Optional Superconvergent Points for the Finite Volume Element Method ⋮ New superconvergent structures developed from the finite volume element method in 1D ⋮ Unified construction and \(L^2\) analysis for the finite volume element method over tensorial meshes

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