Self Adaptive Methods for Parabolic Partial Differential Equations
Gannon, Dennis Brooke
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https://hdl.handle.net/2142/66442
Description
Title
Self Adaptive Methods for Parabolic Partial Differential Equations
Author(s)
Gannon, Dennis Brooke
Issue Date
1980
Department of Study
Computer Science
Discipline
Computer Science
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Computer Science
Language
eng
Abstract
In many applications, the solutions to important partial differential equations are characterized by a sharp active region of transition (such as wave fronts or areas of rapid diffusion) surrounded by relatively calm stable regions. The numerical approximation to such a solution is based on a mesh or grid structure that is best when very fine in the active region and coarse in the calm region.
This work considers algorithms for the proper construction of locally refined grids for finite element based methods for the solution to such problems. By extending the work of Babuska and Rheinboldt to the case of parabolic problems, refinement criteria are developed and tested for this class of problems.
The computational complexity of such a strategy is studied, and algorithms based on nested dissection are presented to solve the associated linear algebra problems.
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