Multiresolution Schemes for Strongly Degenerate Parabolic Equations in One Space Dimension Raimund Bürger, 1 Alice Kozakevicius, 2 Mauricio Sepúlveda 1 1 Departamento 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 Received 1 September 2005; accepted 26 August 2006 Published online 8 January 2007 in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/num.20206 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 dis- cretization, 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 trans- form 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 23: 706–730, 2007 Keywords: multiresolution schemes; strongly degenerate parabolic equations; ENO interpolation; thresholded wavelet transform; thresholding strategy 1. INTRODUCTION 1.1. Scope High-resolution finite volume schemes for conservation laws are at least second-order accurate in regions where the solution is smooth and resolve discontinuities sharply and without spurious oscillations. Such methods are presented, for example, in [1–4]. The multiresolution method has been devised (at least, originally) to reduce the computational cost of these schemes. The solution u of the conservation law u t + f (u) x = 0, (x , t) ∈ Q T :=  ×[0, T ],  ⊆ R (1.1) usually exhibits strong variations (shocks) in small regions but is smooth on the major portion of Q T . The multiresolution technique adaptively concentrates computational effort on the regions Correspondence to: Raimund Bürger, Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Casilla 160-C, Concepción, Chile (e-mail: rburger@ing-mat.udec.cl) © 2007 Wiley Periodicals, Inc.