Two adaptive wavelet algorithms for non-linear parabolic partial differential equations

This paper is concerned with the construction of wavelet based adaptive algorithms for the numerical resolution of evolution equations. The adaptivity is applied into two complementary directions. The first direction shares the approaches involved in classical adaptive finite element methods and is related to a solution dependent definition of spaces of approximation. The second direction is related to the approximation of evolution operators that is made solution dependent following the philosophy of essentially non-oscillatory schemes. After the construction of the schemes, numerical tests are provided. (C) 2002 Elsevier Science Ltd. All rights reserved.