Aspects of quaranteed error control in CPDEs

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Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik

Whenever numerical algorithms are employed for a reliable computational forecast, they need to allow for an error control in the final quantity of interest. The discretisation error control is of some particular importance in computational PDEs (CPDEs) where guaranteed upper error bounds (GUB) are of vital relevance. After a quick overview over energy norm error control in second-order elliptic PDEs, this paper focuses on three particular aspects. First, the variational crimes from a nonconforming finite element discretisation and guaranteed error bounds in the discrete norm with improved postprocessing of the GUB. Second, the reliable approximation of the discretisation error on curved boundaries and, finally, the reliable bounds of the error with respect to some goal-functional, namely, the error in the approximation of the directional derivative at a given point

Guaranteed error control, equilibration error estimators, Poisson model problem, conforming finite element methods, Crouzeix-Raviart nonconforming finite element methods, curved boundaries, guaranteed goal-oriented error control.
Carstensen, C., Merdon, C., & Neumann, J. (2013). Aspects of quaranteed error control in CPDEs (Version publishedVersion, Vol. 1775). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.