@Article{CiCP-6-1,
author = {},
title = {A Bilinear Immersed Finite Volume Element Method for the Diffusion Equation with Discontinuous Coefficient},
journal = {Communications in Computational Physics},
year = {2009},
volume = {6},
number = {1},
pages = {185--202},
abstract = {<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>},
issn = {1991-7120},
doi = {https://doi.org/2009-CiCP-7677},
url = {https://global-sci.com/article/81140/a-bilinear-immersed-finite-volume-element-method-for-the-diffusion-equation-with-discontinuous-coefficient}
}