Análise de estimador de erro a posteriori

Abstract

Computational simulations undoubtedly bring numerical errors alongside them, even if the mathematical model is sophisticated. Therefore, the theory of error estimation became essential and is gaining space due to the benefits it promotes by providing the simulation basis for the essential physical phenomenon in engineering applications. In certain cases, such as Structural Mechanics, it is also required a degree of reliability and there can not be a benchmark problem for its validation, whereas a posteriori error estimation supplies this aspect of safety. Consequently, the present project wishes to develop and validate an a posteriori error estimator through a model problem based on the Laplace equation. The validation of such estimator requires a comparison within others of the same type and within h refinement types, uniform and adaptive. Promising results of total error were achieved for the proposed estimator, which produces coherent results when compared to a second one. Nonetheless, a more in-depth analysis of computacional processing expenditure is required. Finally, the advancement of this line of research at UTFPR was allowed by the investigation and other subjects are suggested as a form of extension of such studies.