A system of conservation laws including a stiff relaxation term; The 2D case

Wen Shen; Aslak Tveito; Ragnar Winther

doi:10.1007/BF01733792

A system of conservation laws including a stiff relaxation term; The 2D case

Wen Shen, Aslak Tveito, Ragnar Winther

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Abstract

We analyze a system of conservation laws in two space dimensions with a stiff relaxation term. A semi-implicit finite difference method approximating the system is studied and an error bound of order script O sign(√Δt) measured in L¹ is derived. This error bound is independent of the relaxation time δ > 0. Furthermore, it is proved that the solutions of the system converge towards the solution of an equilibrium model as the relaxation time δ tends to zero, and that the rate of convergence measured in L¹ is of order script O sign(δ^1/3). Finally, we present some numerical illustrations.

Original language	English (US)
Pages (from-to)	786-813
Number of pages	28
Journal	BIT Numerical Mathematics
Volume	36
Issue number	4
DOIs	https://doi.org/10.1007/BF01733792
State	Published - Jan 1 1996

All Science Journal Classification (ASJC) codes

Software
Computer Networks and Communications
Computational Mathematics
Applied Mathematics

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10.1007/BF01733792

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N2 - We analyze a system of conservation laws in two space dimensions with a stiff relaxation term. A semi-implicit finite difference method approximating the system is studied and an error bound of order script O sign(√Δt) measured in L1 is derived. This error bound is independent of the relaxation time δ > 0. Furthermore, it is proved that the solutions of the system converge towards the solution of an equilibrium model as the relaxation time δ tends to zero, and that the rate of convergence measured in L1 is of order script O sign(δ1/3). Finally, we present some numerical illustrations.

AB - We analyze a system of conservation laws in two space dimensions with a stiff relaxation term. A semi-implicit finite difference method approximating the system is studied and an error bound of order script O sign(√Δt) measured in L1 is derived. This error bound is independent of the relaxation time δ > 0. Furthermore, it is proved that the solutions of the system converge towards the solution of an equilibrium model as the relaxation time δ tends to zero, and that the rate of convergence measured in L1 is of order script O sign(δ1/3). Finally, we present some numerical illustrations.

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A system of conservation laws including a stiff relaxation term; The 2D case

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