Recently, we devised an approach to a posteriori error analysis, which clarifies the role of oscillation and where oscillation is bounded in terms of the current approximation error. Basing upon this approach, we derive plain convergence of adaptive linear finite elements approximating the Poisson problem. The result covers arbritray $H^{-1}$-data and characterizes convergent marking strategies.
Convergence of Adaptive Finite Element Methods with Error-Dominated Oscillation / C. Kreuzer, A. Veeser (LECTURE NOTES IN COMPUTATIONAL SCIENCE AND ENGINEERING). - In: Numerical Mathematics and Advanced Applications ENUMATH 2017 / [a cura di] F. Radu, K. Kumar, I. Berre, J. Nordbotten, I. Pop. - [s.l] : Springer, Cham, 2019. - ISBN 9783319964140. - pp. 471-479 (( convegno ENUMATH 2017 tenutosi a Voss nel 2017 [10.1007/978-3-319-96415-7_42].
Convergence of Adaptive Finite Element Methods with Error-Dominated Oscillation
A. Veeser
2019
Abstract
Recently, we devised an approach to a posteriori error analysis, which clarifies the role of oscillation and where oscillation is bounded in terms of the current approximation error. Basing upon this approach, we derive plain convergence of adaptive linear finite elements approximating the Poisson problem. The result covers arbritray $H^{-1}$-data and characterizes convergent marking strategies.
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