@Article{IJNAM-17-872, author = {Zhou , Yanhui}, 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} }