ABSTRACT
Error estimation is a key feature of an adaptive procedure. An error estimator should provide information about the global quality of the solution and the distribution of the error in the domain. A priori error estimates are the main tool for the theoretical study of the Finite Element Method but they cannot provide practical results. The residual of the finite element solution is used as a source in local boundary value problems associated with the error. This chapter devotes to draw the main ideas of the linear error estimator. This estimator can only be applied to linear problems. The chapter describes that the linear error estimator is generalized to nonlinear problems. The estimator has been used in adaptive procedures for nonlinear analysis with excellent success. The tangent bilinear form is used both in the residual equation and as a norm allowing measuring the error with a physical interpretation.
