Locally conservative immersed finite element method for elliptic interface problems

by   Gwanghyun Jo, et al.

In this paper, we introduce the locally conservative enriched immersed finite element method (EIFEM) to tackle the elliptic problem with interface. The immersed finite element is useful for handling interface with mesh unfit with the interface. However, all the currently available method under IFEM framework may not be designed to consider the flux conservation. We provide an efficient and effective remedy for this issue by introducing a local piecewise constant enrichment, which provides the locally conservative flux. We have also constructed and analyzed an auxiliary space preconditioner for the resulting system based on the application of algebraic multigrid method. The new observation in this work is that by imposing strong Dirichlet boundary condition for the standard IFEM part of EIFEM, we are able to remove the zero eigen-mode of the EIFEM system while still imposing the Dirichlet boundary condition weakly assigned to the piecewise constant enrichment part of EIFEM. A couple of issues relevant to the piecewise constant enrichment given for the mesh unfit to the interface has been discussed and clarified as well. Numerical tests are provided to confirm the theoretical development.



page 1

page 2

page 3

page 4


An extended mixed finite element method for elliptic interface problems

In this paper, we propose an extended mixed finite element method for el...

Conservative Discontinuous Cut Finite Element Methods

We develop a conservative cut finite element method for an elliptic coup...

A locally modified second-order finite element method for interface problems

The locally modified finite element method, which is introduced in [Frei...

Numerical recovery of the piecewise constant leading coefficient of an elliptic equation

We propose a numerical algorithm for the reconstruction of a piecewise c...

Lowest-degree robust finite element scheme for a fourth-order elliptic singular perturbation problem on rectangular grids

In this paper, a piecewise quadratic nonconforming finite element method...

The Convergence Rate of MsFEM for Various Boundary Problems

In this paper, we give a detailed analysis of the effectiveness of class...

Meshfree Collocation for Elliptic Problems with Discontinuous Coefficients

We present a meshfree generalized finite difference method (GFDM) for so...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.