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Advanced Numerical Methods in the Mathematical Sciences

Xu Zhang, Purdue University
Immersed Finite Element Methods with Enhanced Stability


New immersed finite element (IFE) methods are introduced for the second-order elliptic interface problems. Comparing with classic IFE schemes using Galerkin formulation, the new IFE methods contain additional stabilization terms, which are used to penalize the discontinuity of IFE functions. A priori error estimates show that these new methods converge optimally in energy norm. Numerical experiments indicate that these stabilized IFE methods outperform classic IFE methods in the vicinity of interfaces.