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A RTk - P-k approximation for linear elasticity yielding a broken H(div) convergent postprocessed stress
Fecha
2015
Autores
Resumen
We present a non-standard mixed finite element method for the linear elasticity problem in Rn with non-homogeneous Dirichlet boundary conditions. More precisely, our approach his based on a simplified interpretation of the pseudo stress–displacement formulation originally proposed in Arnold and Falk (1988), which does not require symmetric tensor spaces in the finite element discretization. We apply the classical Babuˇ ska–Brezzi theory to prove that the corresponding continuous and discrete schemes are well-posed. In particular, Raviart–Thomas spaces of orderk≥0 for the pseudo stress and piece wise polynomials of degree ≤k for the displacement can be utilized. In addition, complementing the results in the afore mentioned reference, we introduceanewpostprocessingformulaforthestressrecoveringtheoptimally convergent approximation of the broken H(div)-norm. Numerical results confirm our theoretical findings.