# Optimal Finite Element Methods for Interface Problems

Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 104)

## Abstract

There are many physical problems such as multiphase flows and fluid-structure interactions whose solutions are piecewise smooth but may have discontinuity across some curved interfaces. The direct application of standard finite element method may not perform well. In this paper, we study some special finite element methods for this type of problems. For simplicity of exposition, we consider the case that there is only one interface which is smooth. Let $$\varOmega,\varOmega _{1} \subset \mathbb{R}^{2}$$ be two bounded domains with $$\varOmega _{1} \subset \varOmega$$. We assume that Γ = ∂ Ω1 is sufficiently smooth, and $$\varGamma \cap \partial \varOmega =\emptyset$$. To be focused on the influence of Γ, we assume $$\varOmega = (-1,1)^{2}$$.

## Keywords

Element Space Multigrid Method Linear Element Interpolation Operator Piecewise Smooth Function
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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