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Volume 6, Issue 1
A Family of Characteristic Discontinuous Galerkin Methods for Transient Advection-Diffusion Equations and Their Optimal-Order L2 Error Estimates

Kaixin Wang, Hong Wang, Mohamed Al-Lawatia & Hongxing Rui

Commun. Comput. Phys., 6 (2009), pp. 203-230.

Published online: 2009-06

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  • 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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@Article{CiCP-6-203, author = {Kaixin Wang, Hong Wang, Mohamed Al-Lawatia and Hongxing Rui}, title = {A Family of Characteristic Discontinuous Galerkin Methods for Transient Advection-Diffusion Equations and Their Optimal-Order L2 Error Estimates}, journal = {Communications in Computational Physics}, year = {2009}, volume = {6}, number = {1}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7030.html} }
TY - JOUR T1 - A Family of Characteristic Discontinuous Galerkin Methods for Transient Advection-Diffusion Equations and Their Optimal-Order L2 Error Estimates AU - Kaixin Wang, Hong Wang, Mohamed Al-Lawatia & Hongxing Rui JO - Communications in Computational Physics VL - 1 SP - 203 EP - 230 PY - 2009 DA - 2009/06 SN - 6 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7030.html KW - AB -

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.

Kaixin Wang, Hong Wang, Mohamed Al-Lawatia and Hongxing Rui. (2009). A Family of Characteristic Discontinuous Galerkin Methods for Transient Advection-Diffusion Equations and Their Optimal-Order L2 Error Estimates. Communications in Computational Physics. 6 (1). 203-230. doi:
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