Year: 2008
Numerical Mathematics: Theory, Methods and Applications, Vol. 1 (2008), Iss. 1 : pp. 29–43
Abstract
We prove convergence for a meshfree first-order system least squares (FOSLS)
partition of unity finite element method (PUFEM). Essentially, by virtue of the partition
of unity, local approximation gives rise to global approximation in $\mathrm{H}(div)\cap\mathrm{H}(curl)$.
The FOSLS formulation yields local a posteriori error estimates to guide the judicious
allotment of new degrees of freedom to enrich the initial point set in a meshfree discretization. Preliminary numerical results are provided and remaining challenges are
discussed.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2008-NMTMA-6040
Numerical Mathematics: Theory, Methods and Applications, Vol. 1 (2008), Iss. 1 : pp. 29–43
Published online: 2008-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Meshfree methods first-order system least squares adaptive finite elements.