An Unfitted Interface Penalty Finite EI-Ement Method With Weighted Aver-Age For Elliptic Interface Problems

An unfitted interface penalty finite element method with weighted average for elliptic interface problems is considered. A lot of practical problems can be described by elliptic problems with discontinuous coefficient, such as the heat conduction problem, the distribution of electric field and so on. Such problems with discontinuous coefficients are usually called interface problems. In [45], an hp version of interface penalty finite element method (hp-IPFEM) is proposed for elliptic interface problems in two and three dimensions on unfitted meshes. Error estimates in broken H1-norm, which are optimal with respect to h and suboptimal with respect to p by half an order of p, are derived. Both symmetric and non-symmetric IPFEM are considered. Error estimates in L2-norm are proved by the duality argument. The difference between the method considered in this thesis and that of [45] is that our method uses weighted averages in the bilinear form instead of the arithmetic averages. We remark that the computational cost can be reduced by properly choosing the weights. H1-and L2-error estimates are derived for the IPFEM with weighted average. Numerical examples are provided to illustrate the performance of the method.