Article

Discontinuous Galerkin finite element methods for a forward-backward heat equation

Department of Mathematical Sciences, University of Cincinnati, P.O. Box 210025, Cincinnati, OH 45221, USA
Applied Numerical Mathematics (Impact Factor: 1.04). 09/1998; 28(1):37-44. DOI: 10.1016/S0168-9274(98)00011-7

ABSTRACT A space-time finite element method is introduced to solve a model forward-backward heat equation. The scheme uses the discontinuous Galerkin method for the time discretization. An error analysis for the scheme is presented.

0 Followers
 · 
111 Views
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: A finite difference method is introduced to solve the forward-backward heat equation in two space dimensions. In this procedure, the backward and forward difference scheme in two subdomains and a coarse-mesh second-order central difference scheme at the middle interface are used. Maximum norm error estimate for the procedure is derived. Then an iterative method based on domain decomposition is presented for the numerical scheme and the convergence of the given method is established. Then numerical experiments are presented to support the theoretical analysis. KeywordsForward-backward heat equation-coarse mesh-iterative method MR Subject Classification65N20-65N10-35K05-65N55
    Applied Mathematics 03/2010; 25(1):101-111. DOI:10.1007/s11766-010-1812-1 · 0.27 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We study the numerical solution of the Fokker–Planck equation. This equation gives a good approximation to the radiative transport equation when scattering is peaked sharply in the forward direction which is the case for light propagation in tissues, for example. We derive first the numerical solution for the problem with constant coefficients. This numerical solution is constructed as an expansion in plane wave solutions. Then we extend that result to take into account coefficients that vary spatially. This extension leads to a coupled system of initial and final value problems. We solve this system iteratively. Numerical results show the utility of this method.
    Journal of Quantitative Spectroscopy and Radiative Transfer 03/2008; 109(5):727-740. DOI:10.1016/j.jqsrt.2007.09.011 · 2.29 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: In this article we analyzed the convergence of the Schwarz waveform relaxation method for solving the forward-backward heat equation. Numerical results are presented for a specific type of model problem.
    Journal of Computational and Applied Mathematics 11/2007; 208(2):380-390. DOI:10.1016/j.cam.2006.10.022 · 1.08 Impact Factor

Preview

Download
1 Download