Least-squares finite element methods with element-by-element solution including adaptive refinement
This dissertation contains the basic theory and a systematic procedure for constructing a least-squares finite element method for linear and nonlinear first-order systems of partial differential equations in engineering and mathematical physics. Error estimates, a condition number bound, and the optimal choice for weighting factors for the least squares finite element approximation are presented. The procedure is implemented in conjunction with an element-by-element preconditioned conjugate-gradient method. A new preconditioner is formulated and analyzed. An adaptive refinement strategy is developed and implemented in a series of numerical studies. Applications to practical problems in incompressible and compressible flow analysis are presented.
- Research Organization:
- Texas Univ., Austin (USA)
- OSTI ID:
- 6470589
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
420200 -- Engineering-- Facilities
Equipment
& Techniques
99 GENERAL AND MISCELLANEOUS
990230* -- Mathematics & Mathematical Models-- (1987-1989)
COMPRESSIBLE FLOW
DIFFERENTIAL EQUATIONS
EQUATIONS
FINITE ELEMENT METHOD
FLUID FLOW
INCOMPRESSIBLE FLOW
LEAST SQUARE FIT
MATHEMATICS
MAXIMUM-LIKELIHOOD FIT
NUMERICAL ANALYSIS
NUMERICAL SOLUTION