A posteriori error estimation in large-strain elasticity using equilibrated local Neumann problems Original Research Article

A method to obtain a posteriori an accurate measure of the error in finite element computations is to solve a Neumann problem with equilibrated tractions for each finite element. We extend this approach to large-strain elasticity and mixed finite elements, which are well suited for nearly incompressible rubber-like materials. For an L2-projection of the error in the first Piola-Kirchhoff stress tensor we prove that the estimator provides a guaranteed upper bound without multiplicative constants. Numerical examples confirm the effectiveness for both linear and Ogden material.