Investigation of stability and accuracy of high order generalized finite element methods
Li, Haoyang
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https://hdl.handle.net/2142/49379
Description
Title
Investigation of stability and accuracy of high order generalized finite element methods
Author(s)
Li, Haoyang
Issue Date
2014-05-30T16:41:01Z
Director of Research (if dissertation) or Advisor (if thesis)
Duarte, C. Armando
Department of Study
Civil & Environmental Eng
Discipline
Civil Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Keyword(s)
Generalized Finite Element Method (GFEM)
stable generalized finite element method
convergence analysis
conditioning analysis
high order
polynomial enrichment
Abstract
The Generalized Finite Element methods (GFEMs) is a family of discretization methods which are based on the partition of unity (PoU) concept and are able to provide users with flexibility in choosing enrichments to approximate the target problem. The quality of the resulting approximation can be judged by the accuracy and its convergence rate, the conditioning and its growth rate. A major type of GFEM enrichment is the polynomial enrichment. Based on that, several modified versions of enrichments can be formulated and adopted in the simulation yielding different approximation behaviors in terms of accuracy and conditioning. By solving a one-dimensional problem and a two-dimensional problem, this report compares the numerical behaviors for different discretization methods including p-Lagrange FEM, p-hierarchical FEM, GFEM, stable GFEM (SGFEM) which is a recently proposed method with improved conditioning, and a number of variations on the GFEM and SGFEM. Other aspects considered are the linear dependency (LD) issue, the effect of mesh perturbation, and the factorization time. They are also presented to provide the reader with a broader knowledge of GFEMs.
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