While a priori error estimates tell us about the convergence rate of the numerical method, they do not give a quantitative estimate on the size of the error, which a posteriori error estimates provide. This is essential in evaluating the accuracy of a computed solution with respect to a predefined tolerance level. The a posteriori error estimate allows for adaptive hp-refinement of the numerical method and has a low computational cost since it is computed locally. This talk will present an a posteriori error estimator for the finite element solution to a nonlinear elliptic problem.
Kenny is an Applied Mathematics Honours student working with Thanh Tran.