Summary
In this paper we analyze the behavior of the so-calledp-version of the finite element method when applied to the equations of plane strain linear elasticity. We establish optimal rate error estimates that are uniformly valid, independent of the value of the Poisson ratio,v, in the interval ]0, 1/2[. This shows that thep-versiondoes not exhibit the degeneracy phenomenon which has led to the use of various, only partially justified techniques of reduced integration or mixed formulations for more standard finite element schemes and the case of a nearly incompressible material.
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This work was supported by the Office of Naval Research under Grant # N00014-81-K0002.
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Vogelius, M. An analysis of thep-version of the finite element method for nearly incompressible materials. Numer. Math. 41, 39–53 (1983). https://doi.org/10.1007/BF01396304
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DOI: https://doi.org/10.1007/BF01396304