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A Partition of Unity Method with Penalty for Fourth Order Problems

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Abstract

A partition of unity method for fourth order problems is proposed. As a model problem, we focus on the biharmonic problem with either clamped or simply supported boundary conditions when the domain is a bounded polygon. The algorithm is presented, error estimates are made, and numerical results are shown to verify the error estimates.

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Acknowledgments

The author would like to thank Susanne C. Brenner and Li-Yeng Sung for the helpful conversations in regards to this work.

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Authors and Affiliations

  1. Department of Mathematics and Center for Computation & Technology, Louisiana State University, Baton Rouge, LA , 70803, USA

    Christopher B. Davis

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  1. Christopher B. Davis
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Correspondence to Christopher B. Davis.

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This work was supported in part by the National Science Foundation through the VIGRE Grant 07-39382.

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Davis, C.B. A Partition of Unity Method with Penalty for Fourth Order Problems. J Sci Comput 60, 228–248 (2014). https://doi.org/10.1007/s10915-013-9795-8

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  • DOI: https://doi.org/10.1007/s10915-013-9795-8

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