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Journal of Scientific Computing

Erschienen in:

30.06.2016

An Unconditionally Stable Quadratic Finite Volume Scheme over Triangular Meshes for Elliptic Equations

verfasst von: Qingsong Zou

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2017

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Abstract

In this note, we present and analyze a special quadratic finite volume scheme over triangular meshes for elliptic equations. The scheme is designed with the second degree Gauss points on the edges and the barycenters of the triangle elements. With a novel from-the-trial-to-test-space mapping, the inf–sup condition of the scheme is shown to hold independently of the minimal angle of the underlying mesh. As a direct consequence, the \(H^1\) norm error of the finite volume solution is shown to converge with the optimal order.

Vorheriger Artikel Unconditional Superconvergence Analysis for Nonlinear Parabolic Equation with Nonconforming Finite Element

Nächster Artikel Superconvergent Two-Grid Methods for Elliptic Eigenvalue Problems

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Titel: An Unconditionally Stable Quadratic Finite Volume Scheme over Triangular Meshes for Elliptic Equations
verfasst von: Qingsong Zou
Publikationsdatum: 30.06.2016
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2017
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-016-0244-3

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