A stabilized immersed finite volume element method for elliptic interface problems

摘要

In this paper, we propose a stabilized immersed finite volume element method for solving elliptic interface problems on Cartesian mesh. To improve the classic immersed finite volume element schemes, certain stability terms over interface edges are added. The new schemes presented here have the same global degrees of freedom as their classic counterparts. Optimal error estimates are derived in an energy norm under piecewise H-2 regularity. Numerical examples demonstrate that the stabilized immersed finite volume element schemes are second order accuracy in L-2 norm and the oscillating behavior of L-infinity error can be improved. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.