A posteriori finite element error estimators for parametrized nonlinear boundary value problems

Abstract

Aposteriori error estimators for finite element solutions of multi-parameter nonlinear partial differential equations are based on an element-by-element solution of local linearizations of the nonlinear equation. In general, the associated bilinear form of the linearized problems satisfies a Garding-type inequality. Under appropriate assumptions it is shown that the error estimators are bounded by constant multiples of the true error in a suitable norm. Computational experiments indicate that the estimators are effective, inexpensive, and insensitive to the choice of-the local coordinate system on the solution manifold.