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Error Estimates for a Meshfree Method with Diffuse Derivatives and Penalty Stabilization

Osorio, Mauricio Andres
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1273521053

Abstract Details

2010, PhD, University of Cincinnati, Arts and Sciences : Mathematical Sciences.
A meshfree method with diffuse derivatives in a Galerkin framework is developed for second order partial differential equation problems. A unified treatment of the diffuse derivative and an error analysis for this new method are provided in the case of elliptic boundary value problems with Neumann boundary conditions in one and multiple dimensions. To our knowledge, this is the first time an error analysis of a diffuse derivative scheme with high order accuracy has been done. Computational results for this new scheme in one and two dimensions are also provided and confirm the theoretical convergence rates.
Donald French, PhD (Committee Chair)
Sookkyung Lim, PhD (Committee Member)
Bingyu Zhang, PhD (Committee Member)
92 p.
Mathematics
Meshfree methods; Meshless methods; Error Estimates; Diffuse Derivative; Diffuse Element Method; Moving Least Squares

Recommended Citations

Citations

  • Osorio, M. A. (2010). Error Estimates for a Meshfree Method with Diffuse Derivatives and Penalty Stabilization [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1273521053

    APA Style (7th edition)

  • Osorio, Mauricio. Error Estimates for a Meshfree Method with Diffuse Derivatives and Penalty Stabilization. 2010. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1273521053.

    MLA Style (8th edition)

  • Osorio, Mauricio. "Error Estimates for a Meshfree Method with Diffuse Derivatives and Penalty Stabilization." Doctoral dissertation, University of Cincinnati, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1273521053

    Chicago Manual of Style (17th edition)

ucin1273521053
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This open access ETD is published by University of Cincinnati and OhioLINK.