The Role of Dual Consistency in Functional Accuracy: Error Estimation and Superconvergence

A discretization is dual consistent if it leads to a discrete dual problem that is a consistent approximation of the corresponding continuous dual problem. This paper investigates the impact of dual consistency on high-order summation-by-parts finite-difference schemes. In particular, dual consistent schemes lead to superconvergent functionals and accurate functional error estimates. Numerical examples demonstrate that dual consistent schemes significantly outperform dual inconsistent schemes in terms of functional accuracy and error-estimate effectiveness. The influence of dual consistency on general discretizations is discussed.

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