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Volume 1, Issue 1
Meshfree First-Order System Least Squares

Hugh R. MacMillan, Max D. Gunzburger & John V. Burkardt

Numer. Math. Theor. Meth. Appl., 1 (2008), pp. 29-43.

Published online: 2008-01

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  • 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.

  • Keywords

Meshfree methods, first-order system least squares, adaptive finite elements.

  • AMS Subject Headings

65N30, 65N50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-1-29, author = {Hugh R. MacMillan, Max D. Gunzburger and John V. Burkardt}, title = {Meshfree First-Order System Least Squares}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2008}, volume = {1}, number = {1}, pages = {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.

}, issn = {2079-7338}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/nmtma/6040.html} }
TY - JOUR T1 - Meshfree First-Order System Least Squares AU - Hugh R. MacMillan, Max D. Gunzburger & John V. Burkardt JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 29 EP - 43 PY - 2008 DA - 2008/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/nmtma/6040.html KW - Meshfree methods, first-order system least squares, adaptive finite elements. AB -

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.

Hugh R. MacMillan, Max D. Gunzburger and John V. Burkardt. (2008). Meshfree First-Order System Least Squares. Numerical Mathematics: Theory, Methods and Applications. 1 (1). 29-43. doi:
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