Discontinuous finite element solution of the radiation diffusion equation on arbitrary polygonal meshes and locally adapted quadrilateral grids Academic Article

abstract

• 2014 Elsevier Inc. All rights reserved. In this paper, we propose a piece-wise linear discontinuous (PWLD) finite element discretization of the diffusion equation for arbitrary polygonal meshes. It is based on the standard diffusion form and uses the symmetric interior penalty technique, which yields a symmetric positive definite linear system matrix. A preconditioned conjugate gradient algorithm is employed to solve the linear system. Piece-wise linear approximations also allow a straightforward implementation of local mesh adaptation by allowing unrefined cells to be interpreted as polygons with an increased number of vertices. Several test cases, taken from the literature on the discretization of the radiation diffusion equation, are presented: random, sinusoidal, Shestakov, and Z meshes are used. The last numerical example demonstrates the application of the PWLD discretization to adaptive mesh refinement.

authors

• Ragusa, Jean

published proceedings

• JOURNAL OF COMPUTATIONAL PHYSICS

author list (cited authors)

• Ragusa, J. C.

citation count

• 7

complete list of authors

• Ragusa, Jean C

publication date

• January 2015

publisher

• Elsevier  Publisher

published in

• Journal of Computational Physics  Journal

keywords

• Adaptive Mesh Refinement
• Arbitrary Polygonal Grids
• Discontinuous Finite Element
• Radiation Diffusion
• Symmetric Interior Penalty Method

Digital Object Identifier (DOI)

• 10.1016/j.jcp.2014.09.013

start page

• 195

end page

• 213

volume

• 280

URL

• http://dx.doi.org/10.1016/j.jcp.2014.09.013