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Equidistribution and Optimal Approximation Class

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Domain Decomposition Methods in Science and Engineering XX

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 91))

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Abstract

Local adaptive grid refinement is an important technique in finite element methods. Its study can be traced back to the pioneering work [2] in one dimension. In recent years, mathematicians start to prove the convergence and optimal complexity of the adaptive procedure in multi-dimensions. Dörfler [11] first proved an error reduction in the energy norm for the Poisson equation provided the initial mesh is fine enough.

The work of C. Bacuta was partially supported by NSF DMS-0713125. L. Chen was supported in part by NSF Grant DMS-0811272, DMS-1115961, and in part by DOE Grant DE-SC0006903. J. Xu was supported in part by NSF DMS-0915153, NSFC-10528102, Alexander von Humboldt Research Award for Senior US Scientists and in part by DOE Grant DE-SC0006903.

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Correspondence to Constantin Bacuta .

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Bacuta, C., Chen, L., Xu, J. (2013). Equidistribution and Optimal Approximation Class. In: Bank, R., Holst, M., Widlund, O., Xu, J. (eds) Domain Decomposition Methods in Science and Engineering XX. Lecture Notes in Computational Science and Engineering, vol 91. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35275-1_1

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