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学术报告: Error analysis of Galerkin FEM for nonlinear parabolic equations with low-regularity structure

报告人:南京大学数学系 李步扬副教授

 

报告题目: Error analysis of Galerkin FEM for nonlinear parabolic equations with low-regularity structure

 

报告时间:20140115日下午17:00

 

报告地点:海韵实验楼108

 

报告摘要:We survey current approaches on error analysis of the Galerkin finite element method for nonlinear parabolic equations. For semi-discrete finite element approximations, the traditional approach to optimal error estimates is based on the elliptic Ritz projection, which usually requires that the coefficients possess mixed second-order derivatives and that the solution are smoother than optimal regularity. These conditions are too strong for some models from engineering and physics. Some more advanced approaches, such as analytic semigroups and parabolic projections, require less regularity of the solution. But these approaches are currently restricted to linear parabolic equations with time-independent and smooth coefficients. We shall extend these advanced approaches to nonlinear parabolic equations with time-dependent and nonsmooth coefficients. Stability of the fully discrete FEM for nonlinear parabolic equations will also be discusses.