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On the justification of plate models

Braess, Dietrich; Sauter, Stefan; Schwab, Christoph (2009)

SAM Research Report

In this paper, we will consider the modelling of problems in linear elasticity on thin plates by the models of Kirchhoff--Love and Reissner--Mindlin. A fundamental investigation for the Kirchhoff plate goes back to Morgenstern [Herleitung der Plattentheorie aus der dreidimensionalen Elastizitätstheorie. Arch. Rational Mech. Anal. 4, 145--152 (1959)] and is based on the two-energies principle of Prager and Synge. This was half a centenium ...

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Approximation on Simplices with respect to Weighted Sobolev Norms

Braess, Dietrich; Schwab, Christoph (1999)

SAM Research Report

Inequalities of Jackson and Bernstein type are derived for polynomial approximation on simplices with respect to Sobolev norms. Although we cannot use orthogonal polynomials, sharp estimates are obtained from a decomposition into orthogonal subspaces. The formulas reflect the symmetries of simplices, but comparable estimates on rectangles show that we cannot expect rotational invariance of the terms with derivatives.

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