A CFL-free explicit characteristic interior penalty scheme for linear advection-reaction equations

Kaixin Wang; Hong Wang; Mohamed Al-Lawatia

doi:10.1002/num.20447

A CFL-free explicit characteristic interior penalty scheme for linear advection-reaction equations

Kaixin Wang^*, Hong Wang, Mohamed Al-Lawatia

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

We develop a CFL-free, explicit characteristic interior penalty scheme (CHIPS) for one-dimensional first-order advection-reaction equations by combining a Eulerian-Lagrangian approach with a discontinuous Galerkin framework. The CHIPS method retains the numerical advantages of the discontinuous Galerkin methods as well as characteristic methods. An optimal-order error estimate in the L² norm for the CHIPS method is derived and numerical experiments are presented to confirm the theoretical estimates.

Original language	English
Pages (from-to)	561-595
Number of pages	35
Journal	Numerical Methods for Partial Differential Equations
Volume	26
Issue number	3
DOIs	https://doi.org/10.1002/num.20447
Publication status	Published - May 2010

Keywords

Characteristic methods
Courant-friedrichs-lewy condition
Discontinuous Galerkin method
Eulerian-lagrangian methods
Interior penalty methods

ASJC Scopus subject areas

Analysis
Numerical Analysis
Computational Mathematics
Applied Mathematics

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10.1002/num.20447

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abstract = "We develop a CFL-free, explicit characteristic interior penalty scheme (CHIPS) for one-dimensional first-order advection-reaction equations by combining a Eulerian-Lagrangian approach with a discontinuous Galerkin framework. The CHIPS method retains the numerical advantages of the discontinuous Galerkin methods as well as characteristic methods. An optimal-order error estimate in the L2 norm for the CHIPS method is derived and numerical experiments are presented to confirm the theoretical estimates.",

keywords = "Characteristic methods, Courant-friedrichs-lewy condition, Discontinuous Galerkin method, Eulerian-lagrangian methods, Interior penalty methods",

author = "Kaixin Wang and Hong Wang and Mohamed Al-Lawatia",

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AU - Wang, Kaixin

AU - Wang, Hong

AU - Al-Lawatia, Mohamed

PY - 2010/5

Y1 - 2010/5

N2 - We develop a CFL-free, explicit characteristic interior penalty scheme (CHIPS) for one-dimensional first-order advection-reaction equations by combining a Eulerian-Lagrangian approach with a discontinuous Galerkin framework. The CHIPS method retains the numerical advantages of the discontinuous Galerkin methods as well as characteristic methods. An optimal-order error estimate in the L2 norm for the CHIPS method is derived and numerical experiments are presented to confirm the theoretical estimates.

AB - We develop a CFL-free, explicit characteristic interior penalty scheme (CHIPS) for one-dimensional first-order advection-reaction equations by combining a Eulerian-Lagrangian approach with a discontinuous Galerkin framework. The CHIPS method retains the numerical advantages of the discontinuous Galerkin methods as well as characteristic methods. An optimal-order error estimate in the L2 norm for the CHIPS method is derived and numerical experiments are presented to confirm the theoretical estimates.

KW - Characteristic methods

KW - Courant-friedrichs-lewy condition

KW - Discontinuous Galerkin method

KW - Eulerian-lagrangian methods

KW - Interior penalty methods

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DO - 10.1002/num.20447

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JO - Numerical Methods for Partial Differential Equations

JF - Numerical Methods for Partial Differential Equations

IS - 3

ER -

A CFL-free explicit characteristic interior penalty scheme for linear advection-reaction equations

Abstract

Keywords

ASJC Scopus subject areas

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