Self adaptive methods for parabolic partial differential equations
- 1 August 1980
- report
- Published by Office of Scientific and Technical Information (OSTI)
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. Refinement criteria are developed and tested for parabolic 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. 17 figures, 4 tables.Keywords
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