Seminars on Numerical Algorithms, Analyses, and Applications：Analysis of a finite element method for second order uniformly elliptic PDEs in non-divergence form

Speaker：Weifeng Qiu (City University of Hong Kong)

Time：2026-5-6 10:30

Location：Conference Room C503 at Administration Building at Haiyun Campus

Abstract:

We propose one finite element method for both second order linear uniformly elliptic PDE in non-divergence form and the uniformly elliptic Hamilton-Jacobi-Bellman (HJB) equation. For both linear elliptic PDE in non-divergence form and the HJB equation,  we prove the well-posedness of strong solution in W^{2,p} and optimal convergence in discrete W^{2,p}-norm of the finite element approximation to the strong solution for 1<p<= 2 on convex polyhedra in $R}^d (d=2,3). If the domain is a two dimensional non-convex polygon, p is valid in a more restricted region. Furthermore, we relax the assumptions on the continuity of coefficients of the HJB equation, which have been widely used in literature.