Analysis of a high-order unfitted finite element method for elliptic interface problems

L2-Error Analysis of an Isoparametric Unfitted Finite Element Method for Elliptic Interface Problems

In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. Recently a new unfitted finite element method was introduced which achieves a high order approximation of the geometry for domains which are implicitly described by smooth level set functions. This method ...

The aggregated unfitted finite element method for elliptic problems

Unfitted finite element techniques are valuable tools in different applications where the generation of body-fitted meshes is difficult. However, these techniques are prone to severe ill conditioning problems that obstruct the efficient use of iterative Krylov methods and, in consequence, hinders the practical usage of unfitted methods for realistic large scale applications. In this work, we pr...

High-Order Multiscale Finite Element Method for Elliptic Problems

In this paper, a new high-order multiscale finite element method is developed for elliptic problems with highly oscillating coefficients. The method is inspired by the multiscale finite element method developed in [3], but a more explicit multiscale finite element space is constructed. The approximation space is nonconforming when oversampling technique is used. We use a PetrovGalerkin formulat...

High Order Unfitted Finite Element Methods for Interface Problems and PDEs on Surfaces

A Finite Element Method for Second Order Nonvariational Elliptic Problems

We propose a numerical method to approximate the solution of second order elliptic problems in nonvariational form. The method is of Galerkin type using conforming finite elements and applied directly to the nonvariational (nondivergence) form of a second order linear elliptic problem. The key tools are an appropriate concept of “finite element Hessian” and a Schur complement approach to solvin...