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

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Abstract
A posteriori 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 Gårding—type inequality. Under appropriate assumption 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.