报告题目： Low-degree finite elements on quadrilateral grids
摘要：I will talk about some results on the designing of quadrilateral (or rectangular) finite element methods for second/fourth order problems. Including
(1)a minimal-degree optimal scheme for biharmonic equation;
(2)a lowest-degree robust finite element scheme for perturbation problem;
(3)an optimal scheme for Poisson equation with quadratic polynomials ($P_2$);
(4)lowest-degree polynomial finite elements on quadrilateral grids.
The construction and application of the discretized (original or smoothened) de Rham complex play an important role in motivating and hinting the construction of these new finite element schemes. Some of these newly constructed finite elements may sometimes perform not as well as standard existing ones from some points of view; theoretical analysis will be given then that their performance can generally not be improved.