Songming Hou, Louisiana Tech University

 

Interface problems occur in many multi-physics and multi-phase applications in science and engineering. Prof. Xu-dong Liu, a tenured faculty at math department of UCSB, guided me into this research area in 2002. This talk is in memory of him, who passed away at a young age in 2005. We proposed a non-traditional finite element method for solving elliptic and elasticity interface problems using non-body-fitted mesh. The invertibility of the coefficient matrix for local construction is proved under certain assumptions. The condition number of the large linear system is studied. We presented numerical results in both 2D and 3D. Extensions to parabolic interface problems and nonlinear interface problems will be discussed.