Sobolev方程的新混合元方法数值模拟

Numerical Simulation of A New Mixed Method for Sobolev Equation

建立Sobolev方程的基于H1-Galerkin混合元方法的一个新的数值格式.所提出的格式能够分裂成两个独立的积分微分子格式,不必求解匹配方程系统,得到了最优收敛阶误差估计.将该方法应用到二维和三维形式.并且不必满足LBB相容性条件.最后,数值算例验证所提出方法的有效性.

A new numerical scheme based on the H1-Galerkin mixed finite element method is constructed for Sobolev equation. The proposed procedure can be split into two independent integrodifferential sub-schemes and does not need to solve a coupled system of equations. Optimal error estimates are derived for problems in one dimension space. An extension of the problems in two and three space variables is also discussed. And the proposed method dose not require the LBB consistency condition. Finally,a numerical example is presented to illustrate the effectiveness of the proposed method.