Strong Form Meshfree Collocation Method for Higher Order and Nonlinear Pdes in Engineering Applications

Graduate Thesis Or Dissertation

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Citeable URL: https://scholar.colorado.edu/concern/graduate_thesis_or_dissertations/dr26xx79c

Abstract

The strong form meshfree collocation method based on Taylor approximation and moving least squares is an alternative to finite element methods for solving partial differential equations in engineering applications. This study examines how the proposed alternative method solves (i) higher-order and (ii) nonlinear partial differential equations. First, the proposed method is formulated in Chapter 2 for the general discretization and solution of strong forms of partial differential equations. Chapter 3 presents the convergence and error behavior of the proposed method for the fourth-order Stommel-Munk equation for wind-driven ocean circulation, as well as the numerical solution of this equation on a domain of more realistic geometry representing the Mediterranean Sea. In Chapter 4, the proposed method is used to solve the nonlinear equations governing linear elastic, small-deformation multi-body thermomechanical contact, including a comparison with analytical and finite element solutions for three verification problems.

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