TY - JOUR
T1 - A stabilised finite element method for a fictitious domain problem allowing small inclusions
AU - Barrenechea, Gabriel
AU - Gonzalez Aguayo, Cheherazada
PY - 2017/6/27
Y1 - 2017/6/27
N2 - The purpose of this work is to approximate numerically an elliptic partial differential equation posed on domains with small perforations (or inclusions). The approach is based on the fictitious domain method, and since the method's interest lies in the case in which the geometrical features are not resolved by the mesh, we propose a stabilised finite element method. The stabilisation term is a simple, non-consistent penalisation, that can be linked to the Barbosa-Hughes approach. Stability and optimal convergence are proved, and numerical results confirm the theory.
AB - The purpose of this work is to approximate numerically an elliptic partial differential equation posed on domains with small perforations (or inclusions). The approach is based on the fictitious domain method, and since the method's interest lies in the case in which the geometrical features are not resolved by the mesh, we propose a stabilised finite element method. The stabilisation term is a simple, non-consistent penalisation, that can be linked to the Barbosa-Hughes approach. Stability and optimal convergence are proved, and numerical results confirm the theory.
KW - partial differential equations
KW - elliptic problems
KW - Navier-Stokes equation
UR - http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1098-2426
M3 - Article
SN - 0749-159X
JO - Numerical Methods for Partial Differential Equations
JF - Numerical Methods for Partial Differential Equations
ER -