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.