Time continuous Galerkin methods for linear heat conduction problems

A Petrov-Galerkin formulation of the semidiscrete linear transient heat con duction problem is given, from which a unified set of A-stable higher-order time integration methods is derived. Accuracy and stability properties can be controlled by an algorithmic parameter introduced in the definition of the test functions. In this manner. A-stable algorithms of order 2p and L-s table algorithms of order 2p - 1 are derived from a unique formulation. In addition, algorithms with intermediate accuracy and stability properties ar e made available. The effects of varying the algorithmic parameter are inve stigated. Numerical tests are included to support the theoretical analysis. (C) 2000 Elsevier Science S.A. All rights reserved.