@Article{JCM-38-547, author = {Awanou , GerardLi , Hengguang and Malitz , Eric}, title = {A Two-Grid Method for the C0 Interior Penalty Discretization of the Monge-Ampère Equation}, journal = {Journal of Computational Mathematics}, year = {2020}, volume = {38}, number = {4}, pages = {547--564}, abstract = {

The purpose of this paper is to analyze an efficient method for the solution of the nonlinear system resulting from the discretization of the elliptic Monge-Ampère equation by a $C^0$ interior penalty method with Lagrange finite elements. We consider the two-grid method for nonlinear equations which consists in solving the discrete nonlinear system on a coarse mesh and using that solution as initial guess for one iteration of Newton's method on a finer mesh. Thus both steps are inexpensive. We give quasi-optimal $W^{1,\infty}$ error estimates for the discretization and estimate the difference between the interior penalty solution and the two-grid numerical solution. Numerical experiments confirm the computational efficiency of the approach compared to Newton's method on the fine mesh.


}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1901-m2018-0039}, url = {http://global-sci.org/intro/article_detail/jcm/16462.html} }