Boundary concentrated finite element methods

摘要

A method with optimal ( up to logarithmic terms) complexity for solving elliptic problems is proposed. The method relies on interior regularity, but the solution may have globally low regularity due to rough boundary data or geometries. Elliptic regularity results, high order approximation results, and an efficient preconditioner are presented. The method is utilized to realize, with linear-logarithmic complexity, an accurate and data-sparse approximation to the associated elliptic Poincare-Steklov operators. Further applications include the treatment of exterior boundary value problems and the solution of problems in the framework of domain decomposition methods. [References: 45]