TY - JOUR T1 - A Class of Bubble Enriched Quadratic Finite Volume Element Schemes on Triangular Meshes AU - Zhou , Yanhui 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.