Volume 17, Issue 6
A Class of Bubble Enriched Quadratic Finite Volume Element Schemes on Triangular Meshes

​Yanhui Zhou

DOI:

Int. J. Numer. Anal. Mod., 17 (2020), pp. 872-899.

Published online: 2020-10

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  • 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.

  • Keywords

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

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-17-872, author = {​Yanhui Zhou , }, title = {A Class of Bubble Enriched Quadratic Finite Volume Element Schemes on Triangular Meshes}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2020}, volume = {17}, number = {6}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/18356.html} }
TY - JOUR T1 - A Class of Bubble Enriched Quadratic Finite Volume Element Schemes on Triangular Meshes AU - ​Yanhui Zhou , JO - International Journal of Numerical Analysis and Modeling VL - 6 SP - 872 EP - 899 PY - 2020 DA - 2020/10 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/18356.html KW - Bubble enriched quadratic finite volume element schemes, anisotropic diffusion problems, triangular meshes, $H^1$ and $L^2$ error estimates. AB -

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.

​Yanhui Zhou. (2020). A Class of Bubble Enriched Quadratic Finite Volume Element Schemes on Triangular Meshes. International Journal of Numerical Analysis and Modeling. 17 (6). 872-899. doi:
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