Time continuous Galerkin methods for linear heat conduction problems Original Research Article

A Petrov–Galerkin formulation of the semidiscrete linear transient heat conduction 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-stable algorithms of order 2p−1 are derived from a unique formulation. In addition, algorithms with intermediate accuracy and stability properties are made available. The effects of varying the algorithmic parameter are investigated. Numerical tests are included to support the theoretical analysis.