Date of Award:
5-1982
Document Type:
Thesis
Degree Name:
Master of Science (MS)
Department:
Mathematics and Statistics
Department name when degree awarded
Mathematics
Committee Chair(s)
Chris Coray
Committee
Chris Coray
Committee
Lawrence Cannon
Committee
Russell Thompson
Committee
Ian Anderson
Abstract
This paper surveys reasons why the Ritz method and the Galerkin method are not efficient and why these methods can not be applied directly, for time dependent problems. It also introduces methods that are used for those problems. For a linear boundary value problem defined by a positive definite symmetric (self-adjoint) operator, the existence and the convergence of the Ritz approximation are guaranteed. In non-symmetric case, Lax-Milgram lemma assures the existence and the convergence of the Galerkin approximation for H1/2(Ω)-elliptic operator. Since time-dependent problems are hyperbolic or parabolic, the existence and the convergence of approximations by those methods are not guaranteed. Moreover, those methods were originally developed for boundary value problems. Thus new techniques are introduced in order to extend those methods to initial-boundary value problems.
Checksum
0db00485ae3f5bb9d39357affa274b88
Recommended Citation
Watanabe, Masaji, "Numerical Methods (Finite Element) for Time-Dependent Partial Differential Equations" (1982). All Graduate Theses and Dissertations, Spring 1920 to Summer 2023. 6978.
https://digitalcommons.usu.edu/etd/6978
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