Stable hp mixed finite elements based on the Hellinger–Reissner principle |
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Institution: | Department of Mathematics and Statistics, University of Maryland, Baltimore County, 1000, Hilltop Circle, Baltimore, MD 21250, USA |
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Abstract: | In the Hellinger–Reissner formulation for linear elasticity, both the displacement u and the stress σ are taken as unknowns, giving rise to a saddle point problem. We present new pairings of quadrilateral ‘trunk’ finite element spaces for this method and prove stability (and optimality) in terms of both h and p. The effect of mesh shape regularity on the stability constant is explicitly tracked. Our results provide a theoretical basis for recent numerical experiments (in the context of a mixed p formulation for viscoelasticity) that showed these spaces worked well computationally. |
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