A weak Galerkin method for second order elliptic problems with polynomial reduction |
| |
Authors: | Nolisa Malluwawadu and Saqib Hussain |
| |
Institution: | Department of Mathematics and Statistics, University of Arkansas at Little Rock, Little Rock, AR, 72204, USA,Department of Mathematics and Statistics, University of Arkansas at Little Rock, Little Rock, AR, 72204, USA |
| |
Abstract: | The second order elliptic equation, which is also know as the diffusion-convection equation, is of great interest in many branches of physics and industry. In this paper, we use the weak Galerkin finite element method to study the general second order elliptic equation. A weak Galerkin finite element method is proposed and analyzed. This scheme features piecewise polynomials of degree $k\geq 1$ on each element and piecewise polynomials of degree $k-1\geq 0$ on each edge or face of the element. Error estimates of optimal order of convergence rate are established in both discrete $H^1$ and standard $L^2$ norm. The paper also presents some numerical experiments to verify the efficiency of the method. |
| |
Keywords: | Galerkin finite element methods second-order elliptic problems discrete gradient mixed finite element methods |
|
| 点击此处可从《Journal of Applied Analysis & Computation》浏览原始摘要信息 |
| 点击此处可从《Journal of Applied Analysis & Computation》下载免费的PDF全文 |
|