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Volume 6, Issue 1
A Bilinear Immersed Finite Volume Element Method for the Diffusion Equation with Discontinuous Coefficient

X.-M. He, T. Lin & Y. Lin

Commun. Comput. Phys., 6 (2009), pp. 185-202.

Published online: 2009-06

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  • Abstract

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'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(h2) (in L2 norm) and O(h) (in H1 norm) convergence rates.

  • Keywords

Interface problems, immersed interface, finite volume element, discontinuous coefficient, diffusion equation.

  • AMS Subject Headings

65N15, 65N30, 65N50, 35R05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-6-185, author = {X.-M. He, T. Lin and Y. Lin}, 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 = {

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'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(h2) (in L2 norm) and O(h) (in H1 norm) convergence rates.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7677.html} }
TY - JOUR T1 - A Bilinear Immersed Finite Volume Element Method for the Diffusion Equation with Discontinuous Coefficient AU - X.-M. He, T. Lin & Y. Lin 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 -

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'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(h2) (in L2 norm) and O(h) (in H1 norm) convergence rates.

X.-M. He, T. Lin and Y. Lin. (2009). A Bilinear Immersed Finite Volume Element Method for the Diffusion Equation with Discontinuous Coefficient. Communications in Computational Physics. 6 (1). 185-202. doi:
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