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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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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, University of Delaware, Newark, DE, 19716, USA

    Constantin Bacuta

  2. Department of Mathematics, University of California at Irvine, Irvine, CA, 92617, USA

    Long Chen

  3. Department of Mathematics, Pennsylvania State University, University Park, PA, 16802, USA

    Jinchao Xu

Authors
  1. Constantin Bacuta
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  2. Long Chen
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  3. Jinchao Xu
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Corresponding author

Correspondence to Constantin Bacuta .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, University of California, San Diego, Gilman Drive 9500, La Jolla, 92093-0112, California, USA

    Randolph Bank

  2. , Department of Mathematics, University of California, San Diego, Gilman Drive 9500, La Jolla, 92093-0112, California, USA

    Michael Holst

  3. , Courant Institute of Mathematical, New York University, Mercer Street 251, New York, 10012-1185, New York, USA

    Olof Widlund

  4. , Department of Mathematics, Pennsylvania State University, State College, 16802, Pennsylvania, USA

    Jinchao Xu

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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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