AN A POSTERIORI ERROR ESTIMATOR FOR THE LAME EQUATION BASED ON H(DIV)-CONFORMING STRESS APPROXIMATIONS S. NICAISE?, K. WITOWSKI† , AND B.I. WOHLMUTH† Abstract. We derive a new a posteriori error estimator for the Lame system based on H(div)- conforming elements and equilibrated fluxes. It is shown that the estimator gives rise to an upper bound where the constant is one up to higher order terms. The lower bound is also established using Argyris elements. The reliability and efficiency of the proposed estimator is confirmed by some numerical tests. Key words. equilibrated fluxes, mixed finite elements, a posteriori error estimates, linear elasticity AMS subject classifications. 65N30, 65N15, 65N50 1. Introduction. The finite element methods are commonly used in the nu- merical realization of many problems occurring in engineering applications, like the Laplace equation, the Lame system, the Stokes system, etc.... (see [13, 17]). Adaptive techniques based on a posteriori error estimators have become indispensable tools for such methods. There now exists a large number of publications devoted to the task of analyzing finite element approximations for problems in solid mechanics and obtain- ing locally defined a posteriori error estimates. We refer to the monographs [2, 10, 29] for a good overview on this topic.
- local postprocessing step
- error estimator
- matrix associated
- square integrable functions
- higher order
- lame system
- norm being
- elements ?h
- when using
- elements