A unified and robust mathematical model for compressible and incompressible linear elasticity can be obtained by rephrasing the Herrmann formulation within the Hellinger-Reissner principle. This quasi-optimally converging extension of PEERS (Plane Elasticity Element with Reduced Symmetry) is called Dual-Mixed Hybrid formulation (DMH). Explicit residual-based a posteriori error estimates for DMH are introduced and are mathematically shown to be locking-free, reliable, and efficient. The estimator serves as a refinement indicator in an adaptive algorithm for effective automatic mesh generation. Numerical evidence supports that the adaptive scheme leads to optimal convergence for Lamé and Stokes benchmark problems with singularities.

A posteriori dual-mixed adaptive finite element error control for Lamé and Stokes equations / C. Carstensen, P. Causin, R. Sacco. - In: NUMERISCHE MATHEMATIK. - ISSN 0029-599X. - 101:2(2005), pp. 309-332.

A posteriori dual-mixed adaptive finite element error control for Lamé and Stokes equations

P. Causin
Secondo
;
2005

Abstract

A unified and robust mathematical model for compressible and incompressible linear elasticity can be obtained by rephrasing the Herrmann formulation within the Hellinger-Reissner principle. This quasi-optimally converging extension of PEERS (Plane Elasticity Element with Reduced Symmetry) is called Dual-Mixed Hybrid formulation (DMH). Explicit residual-based a posteriori error estimates for DMH are introduced and are mathematically shown to be locking-free, reliable, and efficient. The estimator serves as a refinement indicator in an adaptive algorithm for effective automatic mesh generation. Numerical evidence supports that the adaptive scheme leads to optimal convergence for Lamé and Stokes benchmark problems with singularities.
adaptive finite element methods ; quasi-incompressible elasticity ; PEERS ; mixed finite element method ; mesh adaption
Settore MAT/08 - Analisi Numerica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/17355
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