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

TL;DR

This paper introduces a new dimension-independent method to enhance numerical simulations of parabolic equations with incompatible initial and boundary data, improving accuracy in higher-dimensional problems.

Contribution

The paper presents a novel, dimension-independent approach for handling incompatible data in parabolic equations, extending beyond previous one-dimensional methods.

Findings

Method improves numerical accuracy for incompatible data

Applicable to any spatial dimension

Comparable precision to existing methods in 1D

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.