We discuss a new construction of 3D anisotropic meshes to improve the finite element approximation of elliptic boundary value problems with singular solutions from the non-smoothness of the domain. These meshes can violate the maximum angle condition. We derive optimal error estimates for the proposed method.

Hengguang Li is currently an Associate Professor in the Department of Physics of Wayne State University(USA). His research is in the area of Applied Mathematics with main focus on Numerical Analysis, Partial Differential Equations, and Scientific Computing. Prof. Li’s work reflects an interplay of rigorous mathematical analysis of PDEs, the estimate and development of numerical methods, and their applications to physics, engineering, and medicine.