非线性双曲型方程的混合有限元两层网格算法  

Two-Grid Scheme for the Mixed Finite Element Approximations of Nonlinear Hyperbolic Equations

作　　者：陈艳萍[1] 王克彦[1] 

机构地区：[1]华南师范大学数学科学学院,广州510631

出　　处：《华南师范大学学报（自然科学版）》2016年第3期1-6,共6页Journal of South China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(91430104;11271145);广东省自然科学基金项目(2015A030313643);华南师范大学研究生创新基金项目(2015lkxm03)

摘　　要：针对一类非线性双曲型方程,利用混合有限元法,构造了1种混合有限元两层网格算法,给出了两网格方法的误差分析.结果表明,当两层网格算法所选取的粗网格和细网格步长满足H=!(h1/2)时,能获得渐近最优的离散逼近解.并用数值例子验证了该混合有限元两层网格算法的有效性.A combination method of mixed finite element method and two-grid scheme is constructed for solving numerically the two-dimensional nonlinear hyperbolic equations. Error estimate are derived in detail. It is shown that two grid algorithm achieve asymptotically optimal approximation of discrete solution as long as the mesh sizes satisfy H =O（ h^1/2）. Numerical example is presented to verify the efficiency and accuracy of the proposed numerical algorithm.

关 键 词：非线性双曲型方程 混合有限元 两层网格算法 误差分析 

分 类 号：O241.1[理学—计算数学]