A global collocation method for two-dimensional rectangular domains

Provatidis, Christopher

doi:10.2140/jomms.2008.3.185

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A global collocation method for two-dimensional rectangular domains

Christopher G. Provatidis

Vol. 3 (2008), No. 1, 185–193

DOI: 10.2140/jomms.2008.3.185

Abstract

This paper proposes the use of a global collocation procedure in conjunction with a previously developed functional set suitable for the numerical solution of Poisson’s equation in rectangular domains. We propose to expand the unknown variable in a bivariate series of monomials $x^{i} y^{j}$ that exist in Pascal’s triangle. We also propose the use of the bivariate Gordon–Coons interpolation, apart from previous intuitive choices of the aforementioned monomials. The theory is sustained by two numerical examples of Dirichlet boundary conditions, in which we find that the approximate solution monotonically converges towards the exact solution.

Keywords

global collocation, Coons interpolation, Poisson's equation

Milestones

Received: 18 March 2007

Revised: 2 August 2007

Accepted: 6 August 2007

Published: 11 March 2008

Authors

Christopher G. Provatidis
National Technical University of Athens School of Mechanical Engineering 9 Iroon Polytechneiou Avenue GR-15773 Athens, Greece
http://users.ntua.gr/cprovat

Vol. 3, No. 1, 2008

Christopher G. Provatidis

Abstract

Keywords

Milestones

Authors