Domain decomposition based finite element verification in linear framework

The objective of this work is to obtain an a posteriori estimate of the discretization error of a reference problem. This reference problem is a mechanical problem solved using a finite element analysis in linear elasticity. We use the constitutive relation error based estimator. The construction of admissible fields, which is a pillar of the constitutive relation error method, is revisited using a domain decomposition method. The originality of the present work is the introduction of a simplifying hypothesis that leads to an approximation of the discretization error. The construction of admissible fields, which is global, is then replaced by resolution of several local problems that conduce to lower CPU costs. The key point of this domain decomposition based error estimation is the fact that no inter-subdomain communication is needed. We present and illustrate this strategy and evaluate its benefits.