A Class of Bubble Enriched Quadratic Finite Volume Element Schemes on Triangular Meshes

A Class of Bubble Enriched Quadratic Finite Volume Element Schemes on Triangular Meshes

Year:    2020

Author:    Yanhui Zhou

International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 6 : pp. 872–899

Abstract

In this work, we propose and analyze a class of bubble enriched quadratic finite volume element schemes for anisotropic diffusion problems on triangular meshes. The trial function space is defined as quadratic finite element space by adding a space which consists of element-wise bubble functions, and the test function space is the piecewise constant space. For the class of schemes, under the coercivity result, we proved that $|u − u_h|_1$ = $\mathcal{O}(h^2)$ and $‖u − u_h‖_0$ = $\mathcal{O}(h^3)$, where $u$ is the exact solution and $u_h$ is the bubble enriched quadratic finite volume element solution. The theoretical findings are validated by some numerical examples.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2020-IJNAM-18356

International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 6 : pp. 872–899

Published online:    2020-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    28

Keywords:    Bubble enriched quadratic finite volume element schemes anisotropic diffusion problems triangular meshes $H^1$ and $L^2$ error estimates.

Author Details

Yanhui Zhou