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Numerical scheme for a scalar conservation law with memory
Author(s) -
Peszyńska Małgorzata
Publication year - 2014
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21806
Subject(s) - conservation law , scalar (mathematics) , mathematics , godunov's scheme , convergence (economics) , nonlinear system , partial differential equation , term (time) , kernel (algebra) , stability (learning theory) , advection , scheme (mathematics) , numerical diffusion , numerical analysis , mathematical analysis , computer science , discrete mathematics , geometry , physics , quantum mechanics , machine learning , mechanics , economics , thermodynamics , economic growth
We consider approximation of solutions to conservation laws with memory represented by a Volterra term with a smooth decreasing but possibly unbounded kernel. The numerical scheme combines Godunov method with a treatment of the integral term following from product integration rules. We prove stability for both linear and nonlinear flux functions and demonstrate the expected order of convergence using numerical experiments. The problem is motivated by modeling advective transport in heterogeneous media with subscale diffusion.Copyright © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 239–264, 2014