当前位置: X-MOL 学术Comput. Math. Appl. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
A family of quadratic finite volume element schemes over triangular meshes for elliptic equations
Computers & Mathematics with Applications ( IF 2.9 ) Pub Date : 2019-12-04 , DOI: 10.1016/j.camwa.2019.11.017
Yanhui Zhou , Jiming Wu

In this paper, we construct and analyze a family of quadratic finite volume element schemes over triangular meshes for elliptic equations. This family of schemes cover some existing quadratic schemes. For these schemes, by element analysis, we find that each element matrix can be split as two parts : the first part is the element stiffness matrix of the standard quadratic finite element method, while the second part is a tensor product of two vectors. Thanks to this finding, we obtain a sufficient condition to ensure the existence, uniqueness and coercivity result of the finite volume element solution on triangular meshes. More interesting is that, the above condition has a simple and analytic expression, and only relies on the interior angles of each triangular element. Based on this result, a minimum angle condition, better than some existing ones, can be obtained. Moreover, based on the coercivity result, we prove that the finite volume element solution converges to the exact solution with an optimal convergence rate in H1 norm. Finally, some numerical examples are provided to validate the theoretical findings.



中文翻译:

椭圆方程组上三角形网格上的二次有限体积单元格式

在本文中,我们构建并分析了三角形网格上椭圆方程的一类二次有限体积单元方案。这套方案涵盖了一些现有的二次方案。对于这些方案,通过元素分析,我们发现每个元素矩阵都可以分为两部分:第一部分是标准二次有限元方法的元素刚度矩阵,而第二部分是两个向量的张量积。由于这一发现,我们获得了充分的条件来确保三角形网格上有限体积单元解的存在性,唯一性和矫顽性结果。更有趣的是,上述条件具有简单的解析表达式,并且仅依赖于每个三角形元素的内角。根据这个结果,最小角度条件 可以获得比某些现有产品更好的产品。此外,基于矫顽力结果,我们证明了有限体积单元解以最优收敛速度收敛于精确解。H1个规范。最后,提供了一些数值例子来验证理论结果。

更新日期:2020-03-24
down
wechat
bug