题  目：Convergence of FEMs for the dynamic Ginzburg-Landau equations in nonsmooth domains

报告人：Buyang Li Department of Mathematics, Nanjing University

时  间：2015年12月21日     下午 14:30-15:30

地  点：管理科研楼 1611室

报告摘要：
We study convergence of finite element methods for the time-dependent Ginzburg-Landau equations (TDGL) in nonsmooth domains. By establishing existence, uniqueness and regularity of the solution, we see that the solution of the problem is not in $H^1$ if the computational domain contains reentrant corners, and so the finite element method (FEM) may give incorrect solutions. To overcome this difficulty, in arbitrary 2D polygons we reformulate the equations into an equivalent system of elliptic and parabolic equations based on the Hodge decomposition, which avoids direct calculation of the magnetic potential. The reformulated system admit $H^1$ solutions and so it can be solved correctly by the FEM. A decoupled and linearized FEM is introduced to solve the reformulated equations, and error estimates are carried out based on the proved regularity of the solution. Numerical examples are provided to support our theoretical analysis and show the efficiency of the method. In 3D nonsmooth domains, a mixed FEM is introduced to solve the equation, and convergence of the numerical solution is proved without regularity assumption on the solution of the PDE problem.