SUMMARYIn one dimension, Petrov-Galerkin nonsymmetric weighting for the convective diffusion equation can be interpreted as an added dissipation. The addition of an appropriate amount of dissipation can therefore give the same oscillation-free solutions as the 'upwinding', Petrov-Galerkin, finite element methods. The 'balancing dissipation' is optimally chosen so that excessive dissipation does not occur. A scheme is presented for extending this approach to two-dimensional problems, and numerical examples show that the new method can be used with improved computational efficiency.

SUMMARYThis paper presents a simple extension of the patch test to mixed formulations to provide the necessary and sufficient conditions for convergence. The general algebraic conditions of Babuska and Brezzi are given a simple form and a conceptual application of the patch tests serves to point out the instability of several well known formulations for incompressible problems. The test is also applied to mixed displacement-strain formulations of elasticity, and limiting formulations are noted.

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SUMMARYThis note introduces certain stress smoothing procedures and the so called 'Loubignac-Cantin' iteration for restoration of momentum balance in the smoothed stress fields. It is shown that this iteration corresponds precisely to the solution of mixed formulations in which the stresses (or strains) and the displacements are used as primary variables. The procedure has a very wide field of application and promises to add considerable accuracy to f.e.m. results by a small additional expenditure.

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