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Multiresolution schemes for strongly degenerate parabolic equations in one space dimension
Author(s) -
Bürger Raimund,
Kozakevicius Alice,
Sepúlveda Mauricio
Publication year - 2007
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.20206
Subject(s) - mathematics , discretization , partial differential equation , method of lines , interpolation (computer graphics) , degenerate energy levels , multiresolution analysis , mathematical analysis , finite volume method , lipschitz continuity , parabolic partial differential equation , boundary value problem , classification of discontinuities , ordinary differential equation , wavelet , differential equation , wavelet transform , differential algebraic equation , computer science , animation , discrete wavelet transform , physics , computer graphics (images) , quantum mechanics , artificial intelligence , mechanics
An adaptive finite volume method for one‐dimensional strongly degenerate parabolic equations is presented. Using an explicit conservative numerical scheme with a third‐order Runge‐Kutta method for the time discretization, a third‐order ENO interpolation for the convective term, and adding a conservative discretization for the diffusive term, we apply the multiresolution method combining two fundamental concepts: the switch between central interpolation or exact computing of numerical flux and a thresholded wavelet transform applied to cell averages of the solution to control the switch. Applications to mathematical models of sedimentation‐consolidation processes and traffic flow with driver reaction, which involve different types of boundary conditions, illustrate the computational efficiency of the new method. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007