Treatment of Incompatible Initial and Boundary Data for Parabolic Equations in Higher Dimension

Abstract

A new method is proposed to improve the numeri- cal simulation of time dependent problems when the initial and boundary data are not compatible. Unlike earlier methods limited to space dimension one, this method can be used for any space dimension. When both methods are applicable (in space dimen- sion one), the improvements in precision are comparable, but the method proposed here is not restricted by dimension.