报告题目：Recovery based finite element methods for nondivergence form PDEs
In this talk, we will consider the numerical approximation of the non-divergence form PDEs with Cordes coefficients. In that case, the well posedness of the model problems can be viewed as the well posedness of a variational problems on H_0^1 \cap H^2. We construct a new recovery operator to overcome the difficulty that the vanishment of the piecewise second derivative of the linear finite element function. We will introduce some properties of this new recovery operator, especially the consistency of the finite element function that is hard to derive for the classical gradient recovery operators. Finally we use the new gradient recovery operator to construct linear finite element methods for the model problems and get the Cea's type error estimation of the numerical schemes.
Dr. Hailong Guo is currently a Senior Lecturer in the School of Mathematics and Statistics at the University of Melbourne in Australia. Prior to joining the University of Melbourne, he was a Visiting Assistant Professor at the University of California, Santa Barbara between 2015 to 2018. Dr. Guo earned his PhD degree from Wayne State University in 2015. His research interests include deep learning and numerical solutions for partial differential equations.