We prove the convergence of an explicit numerical scheme for the discretization of a coupled hyperbolic-parabolic system in two space dimensions. The hyperbolic part is solved by a Lax-Friedrichs method with dimensional splitting, while the parabolic part is approximated by an explicit finite-difference method. For both equations, the source terms are treated by operator splitting. To prove convergence of the scheme, we show strong convergence of the hyperbolic variable, while convergence of the parabolic part is obtained only weakly∗ in L∞. The proof relies on the fact that the hyperbolic flux depends on the parabolic variable through a convolution function. The paper also includes numerical examples that document the theoretically proved convergence and display the characteristic behaviour of the Lotka-Volterra equations.

Rossi, E., Schleper, V. (2016). Convergence of a numerical scheme for a mixed hyperbolic-parabolic system in two space dimensions. MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE, 50(2), 475-497 [10.1051/m2an/2015050].

Convergence of a numerical scheme for a mixed hyperbolic-parabolic system in two space dimensions

ROSSI, ELENA
Primo
;
2016

Abstract

We prove the convergence of an explicit numerical scheme for the discretization of a coupled hyperbolic-parabolic system in two space dimensions. The hyperbolic part is solved by a Lax-Friedrichs method with dimensional splitting, while the parabolic part is approximated by an explicit finite-difference method. For both equations, the source terms are treated by operator splitting. To prove convergence of the scheme, we show strong convergence of the hyperbolic variable, while convergence of the parabolic part is obtained only weakly∗ in L∞. The proof relies on the fact that the hyperbolic flux depends on the parabolic variable through a convolution function. The paper also includes numerical examples that document the theoretically proved convergence and display the characteristic behaviour of the Lotka-Volterra equations.
Articolo in rivista - Articolo scientifico
Coupled equations; Finite difference schemes; Lax-Friedrichs method; Mixed systems of partial differential equations; Nonlocal conservation laws; Numerical analysis;
Numerical analysis; Mixed systems of partial differential equations; Coupled equations; Lax-Friedrichs method; Finite difference schemes; Nonlocal conservation laws
English
1-mar-2016
2016
50
2
475
497
none
Rossi, E., Schleper, V. (2016). Convergence of a numerical scheme for a mixed hyperbolic-parabolic system in two space dimensions. MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE, 50(2), 475-497 [10.1051/m2an/2015050].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/85715
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