Numerical Analysis Group Research Report NA-90/13

K W Morton

Lagrange-Galerkin and characteristic-Galerkin methods provide the means by which the finite element methodology can reap some of the benefits for evolutionary problems that it enjoys for steady problems. There are three rather different formulations -- the direct, the weak and that which leads to the ECG schemes -- each of which has its advantages.

We will report our experience of using these methods for various applications areas. The direct formulation has proved very effective for the incompressible Navier-Stokes equations while the ECG schemes are more appropriate for shocked flows in gas dynamics. For work with enhanced oil recovery problems, on the other hand, the weak formulation has several advantages.

Analysis of model problems will be used to establish key properties of this class of methods and to highlight the differences between alternative formulations.

Key words and phrases:

Lagrange-Galerkin, characteristic-Galerkin, hyperbolic conservation laws, recovery procedures, stability, supraconvergence

The work reported here forms part of the research programme of the Oxford-Reading Institute for Computational Fluid Dynamics.

This paper is not currently available electronically.