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The gradient recovery for finite volume element method on quadrilateral meshes

Yingwei Song|Tie Zhang
대한수학회 (The Korean Mathematical Society)|2016.11|대한수학회지 (Journal of the KMS)|제53권 제6호|pp. 1411-1429

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참고문헌

키워드

finite volume methodsuperconvergenceelliptic problemquadrilateral meshesgradient recovery
주제분류수학

초록

We consider the finite volume element method for elliptic problems using isoparametric bilinear elements on quadrilateral meshes. A gradient recovery method is presented by using the patch interpolation technique. Based on some superclose estimates, we prove that the recovered gradient $R(\nabla u_h)$ possesses the superconvergence: $\|\nabla u-R(\nabla u_h)\|=O(h^2)\|u\|_3$. Finally, some numerical examples are provided to illustrate our theoretical analysis.

Abstract

We consider the finite volume element method for elliptic problems using isoparametric bilinear elements on quadrilateral meshes. A gradient recovery method is presented by using the patch interpolation technique. Based on some superclose estimates, we prove that the recovered gradient $R(\nabla u_h)$ possesses the superconvergence: $\|\nabla u-R(\nabla u_h)\|=O(h^2)\|u\|_3$. Finally, some numerical examples are provided to illustrate our theoretical analysis.

참고문헌 (22)

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