Multiresolution schemes for strongly degenerate parabolic equations in one space dimension |
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Authors: | Raimund Bürger Alice Kozakevicius Mauricio Sepúlveda |
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Affiliation: | 1. Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Casilla 160‐C, Concepción, ChileDepartamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Casilla 160‐C, Concepción, Chile;2. Departamento de Matemática‐CCNE, Universidade Federal de Santa Maria, Faixa de Camobi, km 9, Campus Universitário, Santa Maria, RS, CEP 97105‐900, Brazil;3. Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Casilla 160‐C, Concepción, Chile |
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Abstract: | 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 |
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Keywords: | multiresolution schemes strongly degenerate parabolic equations ENO interpolation thresholded wavelet transform thresholding strategy |
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