Year: 2024
Author: Tao Zhang, Xiaolin Li
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 1 : pp. 24–46
Abstract
A Nitsche-based element-free Galerkin (EFG) method for solving semilinear elliptic problems is developed and analyzed in this paper. The existence and uniqueness of the weak solution for semilinear elliptic problems are proved based on a condition that the nonlinear term is an increasing Lipschitz continuous function of the unknown function. A simple iterative scheme is used to deal with the nonlinear integral term. We proved the existence, uniqueness and convergence of the weak solution sequence for continuous level of the simple iterative scheme. A commonly used assumption for approximate space, sometimes called inverse assumption, is proved. Optimal order error estimates in $L^2$ and $H^1$ norms are proved for the linear and semilinear elliptic problems. In the actual numerical calculation, the characteristic distance $h$ does not appear explicitly in the parameter $β$ introduced by the Nitsche method. The theoretical results are confirmed numerically.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2022-0019
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 1 : pp. 24–46
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Meshless method element-free Galerkin method Nitsche method semilinear elliptic problem error estimate.
Author Details
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A weak Galerkin meshless method for incompressible Navier–Stokes equations
Li, Xiaolin
Journal of Computational and Applied Mathematics, Vol. 445 (2024), Iss. P.115823
https://doi.org/10.1016/j.cam.2024.115823 [Citations: 8]