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An Eulerian‐Lagrangian discontinuous Galerkin method for transient advection‐diffusion equations |
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| Authors: | Kaixin Wang Hong Wang Mohamed Al‐Lawatia |
| Affiliation: | 1. School of Mathematics and System Sciences, Shandong University, Jinan, Shandong 250100, China;2. Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208School of Mathematics and System Sciences, Shandong University, Jinan, Shandong 250100, China;3. Department of Mathematics and Statistics, Sultan Qaboos University, Muscat, P.O. Box 36, Al‐Khod 123, Sultanate of Oman |
| Abstract: | We develop an Eulerian‐Lagrangian discontinuous Galerkin method for time‐dependent advection‐diffusion equations. The derived scheme has combined advantages of Eulerian‐Lagrangian methods and discontinuous Galerkin methods. The scheme does not contain any undetermined problem‐dependent parameter. An optimal‐order error estimate and superconvergence estimate is derived. Numerical experiments are presented, which verify the theoretical estimates.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007 |
| Keywords: | advection‐diffusion equations characteristic methods discontinuous Galerkin methods Eulerian‐Lagrangian methods interior penalty methods |