Cut finite elements for convection in fractured domains

• We develop a cut finite element method (CutFEM) for the convection problem in a so called fractured domain, which is a union of manifolds of different dimensions such that a d dimensional component always resides on the boundary of a d+1 dimensional component. This type of domain can for instance be used to model porous media with embedded fractures that may intersect. The convection problem is formulated in a compact form suitable for analysis using natural abstract directional derivative and divergence operators. The cut finite element method is posed on a fixed background mesh that covers the domain and the manifolds are allowed to cut through a fixed background mesh in an arbitrary way. We consider a simple method based on continuous piecewise linear elements together with weak enforcement of the coupling conditions and stabilization. We prove a priori error estimates and present illustrating numerical examples.

Ämnesord

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

Nyckelord

A priori error estimates

Convection problems

Fractured domains

Galerkin least squares

Mixed-dimensional domains

Fracture

Mesh generation

Piecewise linear techniques

Porous materials

Convection problem

Coupling condition

Directional derivative

Divergence operators

Modeling porous medias

Piecewise linear

Priori error estimate

Finite element method

Publikations- och innehållstyp

ref (ämneskategori)

art (ämneskategori)