Time finite element methods for initial value problems

This paper deals with the formulation, implementation, and application of p otentially powerful temporal finite element approximations for solving init ial value problems. Weighted residual methods using continuous and disconti nuous approximations are developed and their characteristics in terms of ac curacy and stability are presented and discussed. An adaptive time spectral element methodology is proposed for Lagrangian spectral elements and its c omputational performance is demonstrated for stiff systems of ordinary diff erential equations. (C) 2000 IMACS. Published by Elsevier Science B.V. All rights reserved.