A cut finite element method for a model of pressure in fractured media

by   Erik Burman, et al.

We develop a robust cut finite element method for a model of diffusion in fractured media consisting of a bulk domain with embedded cracks. The crack has its own pressure field and can cut through the bulk mesh in a very general fashion. Starting from a common background bulk mesh, that covers the domain, finite element spaces are constructed for the interface and bulk subdomains leading to efficient computations of the coupling terms. The crack pressure field also uses the bulk mesh for its representation. The interface conditions are a generalized form of conditions of Robin type previously considered in the literature which allows the modeling of a range of flow regimes across the fracture. The method is robust in the following way: 1. Stability of the formulation in the full range of parameter choices; and 2. Not sensitive to the location of the interface in the background mesh. We derive an optimal order a priori error estimate and present illustrating numerical examples.


An adaptive high-order unfitted finite element method for elliptic interface problems

We design an adaptive unfitted finite element method on the Cartesian me...

A novel hierarchical multiresolution framework using CutFEM

In this paper, we propose a robust concurrent multiscale method for cont...

Cut finite element discretizations of cell-by-cell EMI electrophysiology models

The EMI (Extracellular-Membrane-Intracellular) model describes electrica...

Dynamic coupling of a finite element solver to large-scale atomistic simulations

We propose a method for efficiently coupling the finite element method w...

Analysis of optimal preconditioners for CutFEM

In this paper we consider a class of unfitted finite element methods for...

A stable and optimally convergent LaTIn-Cut Finite Element Method for multiple unilateral contact problems

In this paper, we propose a novel unfitted finite element method for the...

Topology optimization of transient vibroacoustic problems for broadband filter design using cut elements

The focus of this article is on shape and topology optimization of trans...

Please sign up or login with your details

Forgot password? Click here to reset