2026-09-20T11:44:37Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/66442 2023-07-11 col_2142_5131 col_2142_10761 com_2142_5130 com_2142_10755 com_2142_234

Gannon, Dennis Brooke 2014-12-13T18:02:16Z 2014-12-13T18:02:16Z 10000-01-01 1980 1980 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. Made available in DSpace on 2014-12-13T18:02:16Z (GMT). No. of bitstreams: 1 8108510.pdf: 2432065 bytes, checksum: 397a5ac85a661c6e9e595ae895ed2d37 (MD5) Previous issue date: 1980 Embargo set by: Seth Robbins for item 66620 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 92 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1980. http://hdl.handle.net/2142/66442 (UMI)AAI8108510 eng Computer Science Self Adaptive Methods for Parabolic Partial Differential Equations text Computer Science Computer Science University of Illinois at Urbana-Champaign Dissertation Ph.D.