Finite Element Solution of 2D and 3D Elliptic Problems with Intersected Interfaces

摘要

In this article we present second-order finite element (FE) symmetric approximations for 2D and 3D elliptic problems with intersecting interfaces. The discretizations are derived, using two type (2D case) and six type (3D case) linear FE with averaging of the obtained FEM approximations at each grid onde. The convergence and accuracy are discussed theoretically and experimentally. Numerical tests show the feasibility of the schemes.