TY - JOUR
T1 - A Bilinear Immersed Finite Volume Element Method for the Diffusion Equation with Discontinuous Coefficient
JO - Communications in Computational Physics
VL - 1
SP - 185
EP - 202
PY - 2009
DA - 2009/06
SN - 6
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cicp/7677.html
KW - Interface problems, immersed interface, finite volume element, discontinuous coefficient, diffusion equation.
AB - <p style="text-align: justify;">This paper is to present a finite volume element (FVE) method based on the
bilinear immersed finite element (IFE) for solving the boundary value problems of the
diffusion equation with a discontinuous coefficient (interface problem). This method
possesses the usual FVE method&#39;s local conservation property and can use a structured
mesh or even the Cartesian mesh to solve a boundary value problem whose coefficient
has discontinuity along piecewise smooth nontrivial curves. Numerical examples are
provided to demonstrate features of this method. In particular, this method can produce
a numerical solution to an interface problem with the usual O(h<sup>2</sup>) (in L<sup>2</sup> norm)
and O(h) (in H<sup>1</sup> norm) convergence rates.</p>