A Petrov-Galerkin transformation that eliminates spurious oscillations forheterogeneous diffusion-reaction equations

In this paper a transformation technique is developed for diffusion-reactio n equations of autocatalytic type, which possess spatially variable coeffic ients, that removes the possibility of spurious oscillations when using a b ackward Euler rime discretization with large time steps. The approach can b e considered as a construction of "special shape functions" yielding a stab le Petrov-Galerkin type approximation. (C) 2001 Elsevier Science B.V. All r ights reserved.