求解广义Burgers-Huxley方程和广义Burgers-Fisher方程的一类局部间断Petrov-Galerkin方法研究  

A LOCAL DISCONTINUOUS PETROV-GALERKIN METHOD FOR THE GENERALIZED BURGERS-HUXLEY EQUATION AND BURGERS-FISHER EQUATION

作　　者：赵国忠[1] 郭怀民[1] 郭鹏云[1] 田兵[1] Zhao Guozhong;Guo Huaimin;Guo Pengyun;Tian Bing(Faculty of Mathematics,Baotou Teachers College,Baotou 014030)

机构地区：[1]包头师范学院数学科学学院,包头014030

出　　处：《高等学校计算数学学报》2020年第3期193-208,共16页Numerical Mathematics A Journal of Chinese Universities

基　　金：The National Natural Science Foundation of China(Grant Nos.11761054,11261035);the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(Grant No.NJYT-15-A07);the Natural Science Foundation of Inner Mongolia Autonomous Region(Grant Nos.2015MS0108,2012MS0102).

摘　　要：In this paper,we proposed a local discontinuous Petrov-Galerkin method for the generalized Burgers-Huxley equation and the generalized Burgers-Fisher equation.The stability analysis of the method is derived for two special cases.The method can choose different trial and test function spaces and preserve the advantage of discontinuous finite element method.Furthermore,the method is easier to accomplished since its computational formula is simpler than the local discontinuous Galerkin method when test function space is chosen as piecewise constant space.Several examples with various parameters are chosen to show the performance of the method.

关 键 词：generalized Burgers-Huxley equation generalized Burgers-Fisher equation local Discontinuous Petrov-Galerkin method convergence order numerical flux 

分 类 号：O241.82[理学—计算数学]