A Family of Characteristic Discontinuous Galerkin Methods for Transient Advection-Diffusion Equations and Their Optimal-Order L<sup>2</sup> Error Estimates

A Family of Characteristic Discontinuous Galerkin Methods for Transient Advection-Diffusion Equations and Their Optimal-Order L<sup>2</sup> Error Estimates

Year:    2009

Communications in Computational Physics, Vol. 6 (2009), Iss. 1 : pp. 203–230

Abstract

We develop a family of characteristic discontinuous Galerkin methods for transient advection-diffusion equations, including the characteristic NIPG, OBB, IIPG, and SIPG schemes. The derived schemes possess combined advantages of Eulerian-Lagrangian methods and discontinuous Galerkin methods. An optimal-order error estimate in the L2 norm and a superconvergence estimate in a weighted energy norm are proved for the characteristic NIPG, IIPG, and SIPG scheme. Numerical experiments are presented to confirm the optimal-order spatial and temporal convergence rates of these schemes as proved in the theorems and to show that these schemes compare favorably to the standard NIPG, OBB, IIPG, and SIPG schemes in the context of advection-diffusion equations.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2009-CiCP-7030

Communications in Computational Physics, Vol. 6 (2009), Iss. 1 : pp. 203–230

Published online:    2009-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    28

Keywords: