Decoupled smooth interfaces for spectral-element approximations of parabolic or elliptic type

A method is examined to approximate the interface conditions for Chebyshev polynomial approximations to the solutions of parabolic problems, and a smoothing technique is used to calculate the interface conditions for a domain decomposition method. The methods uses a polynomial of one less degree then the full approximation to calculate the first derivative so that interface values can be calculated by using only the adjacent subdomains. Theoretical results are given for the consistency of the scheme and practical results are presented. Computational results are given for both a fourth-order Runga-Kutta methods and an explicit/implicit scheme. © 1993 John Wiley & Sons, Inc.