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报告时间：2016.7.6（周三） 上午10:00          地点：理科楼407

报告题目：Recent Development of $L^p$ analysis of finite element parabolic system

报告摘要：In this talk, we present a review of recent development of $L^p$ error estimates of Galerkin FEMs for parabolic equations. The classical energy approach relies heavily on the strong regulairty assumption of the diffusion coefficient, which may not be satisfied in many physical applications. We first established the discrete maximal $L^p$ regularity for a linear parabolic equation with nonsmooth time-dependent diffusion coefficient in a polygon or polyhedron. With the proved discrete maximal $L^p$-regulairty, we then established an optimal $L^p$ eror estimate and an almost optimal $L^\infty$ eror estimate of the finite element solution for nonlinear parabolic equations