Guaranteed computable bounds for the exact error in the finite element solution. I: One-dimensional model problem
The objective of the paper is to illustrate the concepts and the procedure to compute the bounds for the energy norm of the exact error in the finite element solution, and the exact error in any bounded linear functional. An upper bound for the global energy norm of the error is obtained by employing the exact solutions of the element residual problems. A lower bound is obtained by constructing the gap function for the solutions of element residual problems. Enhanced upper and lower bounds for the global energy norm of the error can be constructed by employing the equilibrium corrections. The approach given in the paper can be employed to obtain the bounds which are close to the energy norm of the exact error for coarse mesh and non-smooth solutions.
scientific article; zbMATH DE number 1383978