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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Acknowledgements
AV gratefully acknowledges the support of the GNCS, which is a part of the Italian INdAM.
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Kreuzer, C., Veeser, A. (2019). Convergence of Adaptive Finite Element Methods with Error-Dominated Oscillation. In: Radu, F., Kumar, K., Berre, I., Nordbotten, J., Pop, I. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2017. ENUMATH 2017. Lecture Notes in Computational Science and Engineering, vol 126. Springer, Cham. https://doi.org/10.1007/978-3-319-96415-7_42
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DOI: https://doi.org/10.1007/978-3-319-96415-7_42
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