A Petrov–Galerkin transformation that eliminates spurious oscillations for heterogeneous diffusion–reaction equations

In this paper a transformation technique is developed for diffusion–reaction equations of autocatalytic type, which possess spatially variable coefficients, that removes the possibility of spurious oscillations when using a backward Euler time discretization with large time steps. The approach can be considered as a construction of “special shape functions” yielding a stable Petrov–Galerkin type approximation.