一类对流占优奇异系数多孔介质方程的局部间断有限元方法研究

摘要

本文研究求解一类对流占优奇异系数多孔介质方程的局部间断有限元方法，给出了处理方程奇异系数的方法和详细的局部间断有限元格式。该方法通过适当改写原方程并引入对流流通量以及扩散流通量，可以有效地抑制传统有限元方法求解对流占优问题在大梯度区域出现的数值伪震荡。数值实验表明该方法能有效求解对流占优奇异系数多孔介质方程。%A local discontinues Galerkin finite element method for the numerical simulation of a convection-dominated equation in porous media with singular coefficient is studied in this paper,and the scheme of the local discontinuous method is given in detail for the singular equation studied. By rewriting the original equation into proper form and introducing the convective and diffusive numerical fluxes,the method can effectively overcome numerical oscillation occurred in case of convection-dominated problems. Numerical results are also given to show the effectiveness of the method.