MFE revisited : part 1: adaptive grid-generation using the heat equation

Abstract

In this paper the moving-nite-element method (MFE) is used to solve the heat equation, with an articial time component, to give a non-uniform (steady-state) grid that is adapted to a given prole. It is known from theory and experiments that MFE, applied to parabolic PDEs, gives adaptive grids which satisfy an equidistribution type law. This property is used to create non-uniform nite-element grids that are dictated by second-order derivatives of the solution. The proposed procedure could be used to create an initial grid for MFE itself, to dene a regridding strategy for MFE in case of a distorted grid, or to prescribe a new adaptive grid method where the heat quation is used as a "monitor function".