Abstract
In this survey contribution, we present and compare, from the viewpoint of adaptive computation, several recently published error estimation procedures for the numerical solution of biharmonic and some further fourth order elliptic problems mostly in 2D. In the hp-adaptive finite element method, there are two possibilities to assess the error of the computed solution a posteriori: to construct a classical analytical error estimate or to obtain a more accurate reference solution by the same procedure as the approximate solution and, from it, the computational error estimate. For the lack of space, we sometimes only refer to the notation introduced in the papers quoted. The complete hypotheses and statements of the theorems presented should also be looked for there.
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Acknowledgements
This research was supported by the Grant Agency of the Academy of Sciences of the Czech Republic under Grant IAA100190803 and by the Academy of Sciences of the Czech Republic under Research Plan AV0Z10190503 of the Institute of Mathematics.
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Segeth, K. (2013). On the Advantages and Drawbacks of A Posteriori Error Estimation for Fourth-Order Elliptic Problems. In: Repin, S., Tiihonen, T., Tuovinen, T. (eds) Numerical Methods for Differential Equations, Optimization, and Technological Problems. Computational Methods in Applied Sciences, vol 27. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5288-7_8
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DOI: https://doi.org/10.1007/978-94-007-5288-7_8
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