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Multiresolution schemes for strongly degenerate parabolic equations in one space dimension. (English) Zbl 1114.65120

Summary: 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 essentially nonoscillatory 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.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35K65 Degenerate parabolic equations
35K55 Nonlinear parabolic equations
65T60 Numerical methods for wavelets
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