A Crank-Nicolson finite volume element method for two-dimensional Sobolev equations

Journal of inequalities and applications

Zhendong Luo¹ 

关键词: Crank-Nicolson formulation;    Sobolev equation;    finite volume element method;    error estimates;    numerical simulation;    65M60;    65M15;    65N30;   

DOI  :  10.1186/s13660-016-1131-z

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we provide a new type of study approach for the two-dimensional (2D) Sobolev equations. We first establish a semi-discrete Crank-Nicolson (CN) formulation with second-order accuracy about time for the 2D Sobolev equations. Then we directly establish a fully discrete CN finite volume element (CNFVE) formulation from the semi-discrete CN formulation about time and provide the error estimates for the fully discrete CNFVE solutions. Finally, we provide a numerical example to verify the correction of theoretical conclusions. Further, it is shown that the fully discrete CNFVE formulation is better than the fully discrete FVE formulation with first-order accuracy in time.

【 授权许可】

CC BY