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