A two-grid discretization method for decoupling systems of partial differential equations |
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| Authors: | Jicheng Jin Shi Shu Jinchao Xu |
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| Institution: | Institute for Computational and Applied Mathematics and Department of Mathematics, Xiangtan University, People's Republic of China ; Institute for Computational and Applied Mathematics and Department of Mathematics, Xiangtan University, People's Republic of China ; Institute for Computational and Applied Mathematics, Xiangtan University, People's Republic of China; and Center for Computational Mathematics and Applications, Pennsylvania State University, Pennsylvania |
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| Abstract: | In this paper, we propose a two-grid finite element method for solving coupled partial differential equations, e.g., the Schrödinger-type equation. With this method, the solution of the coupled equations on a fine grid is reduced to the solution of coupled equations on a much coarser grid together with the solution of decoupled equations on the fine grid. It is shown, both theoretically and numerically, that the resulting solution still achieves asymptotically optimal accuracy. |
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| Keywords: | Schr\"{o}dinger type equation coupled system finite element method two-grid |
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