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Theoretical Analysis for Moving Least Square Method with Second Order Pseudo-Derivatives and Stabilization

Clack, Jhules
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1418910272

Abstract Details

2014, PhD, University of Cincinnati, Arts and Sciences: Mathematical Sciences.
Meshfree and, in particular Moving Least Square (MLS) schemes have been used to solve a wide range of partial differential equation problems. It is hoped that the expense of grid generation can be avoided by using these approaches especially in applications where mesh refinement is needed to handle singular solution behavior or, in problems with highly complicated domains. Pseudo or diffuse derivatives (DDs) can be used to reduce computation time in these schemes. The property that these derivatives algebraic form is similar to the MLS functional form, has been exploited in fluid dynamics and elasticity problems to simplify the formulations dramati- cally. Many computational studies show these schemes are accurate but little has been proved or shown in any sort of theoretical manner. In this work we develop a convergence analysis for MLS/DD methods on elliptic boundary value problems. We expand our study incorporating various extensions into simple fractional initial value problems.
Donald French, Ph.D. (Committee Chair)
Sookkyung Lim, Ph.D. (Committee Member)
Stephan Pelikan, Ph.D. (Committee Member)
59 p.
Mathematics
mesh refinement; Moving Least Square

Recommended Citations

Citations

  • Clack, J. (2014). Theoretical Analysis for Moving Least Square Method with Second Order Pseudo-Derivatives and Stabilization [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1418910272

    APA Style (7th edition)

  • Clack, Jhules. Theoretical Analysis for Moving Least Square Method with Second Order Pseudo-Derivatives and Stabilization. 2014. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1418910272.

    MLA Style (8th edition)

  • Clack, Jhules. " Theoretical Analysis for Moving Least Square Method with Second Order Pseudo-Derivatives and Stabilization." Doctoral dissertation, University of Cincinnati, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1418910272

    Chicago Manual of Style (17th edition)

ucin1418910272
321
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This open access ETD is published by University of Cincinnati and OhioLINK.