Virtual element method for nonlinear Sobolev equation on polygonal meshes | |
Article; Early Access | |
关键词: SUPERCONVERGENCE ANALYSIS; GALERKIN METHOD; STOKES PROBLEM; APPROXIMATION; | |
DOI : 10.1007/s11075-023-01553-6 | |
来源: SCIE |
【 摘 要 】
In this work, the virtual element method (VEM) on convex polygonal meshes for the nonlinear Sobolev equations is developed, where the semi-discrete and fully discrete formulations are presented and analyzed. To overcome the complexity of nonlinear terms, the nonlinear coefficient is approximated by employing the orthogonal L-2 projection operator, which is directly computable from the degrees of freedom. Under some assumptions about the nonlinear coefficient, the existence and uniqueness of the semi-discrete solution are analyzed. Furthermore, a priori error estimate showing optimal order of convergence with respect to the H-1 semi-norm was derived. Finally, some numerical experiments are conducted to illustrate the theoretical convergence rate.
【 授权许可】
Free