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Journal of Scientific Computing

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30-06-2016

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

Author: Qingsong Zou

Published in: Journal of Scientific Computing | Issue 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.

previous article Unconditional Superconvergence Analysis for Nonlinear Parabolic Equation with Nonconforming Finite Element

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Title: An Unconditionally Stable Quadratic Finite Volume Scheme over Triangular Meshes for Elliptic Equations
Author: Qingsong Zou
Publication date: 30-06-2016
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 1/2017
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-016-0244-3

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