Publication Results

Code: MOX 32
Title: A Posteriori Dual-Mixed (Hybrid) Adaptive Finite Element Error Control for Lamé and Stokes Equations
Date: Monday 8th March 2004
Author(s) : Carstensen, Carsten; Causin, Paola; Sacco, Riccardo
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Abstract: A unified and robust mathematical model for compressible and incompressible elasticity can be obtained by rephrasing the Hermann formulation within the Hellinger-Reissner principle. The 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 DMII 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.