2018/04/11 by Gerard Awanou, Awanou, Gerard, Hengguang Li +3
Engineering · Mathematics · Medicine · #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical Analysis (math.NA) #Pelvic and Acetabular Injuries
paper · pdf · doi:10.48550/arxiv.1804.04279
openalex publication_date 2018/04/11 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
The purpose of this paper is to analyze an efficient method for the solution\nof the nonlinear system resulting from the discretization of the elliptic\nMonge-Amp `ere equation by a C0 interior penalty method with Lagrange finite\nelements. We consider the two-grid method for nonlinear equations which\nconsists in solving the discrete nonlinear system on a coarse mesh and using\nthat solution as initial guess for one iteration of Newton's method on a finer\nmesh. Thus both steps are inexpensive. We give quasi-optimal W1,\∞\nerror estimates for the discretization and estimate the difference between the\ninterior penalty solution and the two-grid numerical solution. Numerical\nexperiments confirm the computational efficiency of the approach compared to\nNewton's method on the fine mesh.\n