New mixed finite-element methods

Thesis/Dissertation · Thu Jan 01 00:00:00 EST 1987

OSTI ID:6584422

Franca, L P

New finite-element methods are proposed for mixed variational formulations. The methods are constructed by adding to the classical Galerkin method various least-squares like terms. The additional terms involve integrals over element interiors, and include mesh-parameter dependent coefficients. The methods are designed to enhance stability. Consistency is achieved in the sense that exact solutions identically satisfy the variational equations.Applied to several problems, simple finite-element interpolations are rendered convergent, including convenient equal-order interpolations generally unstable within the Galerkin approach. The methods are subdivided into two classes according to the manner in which stability is attained: (1) circumventing Babuska-Brezzi condition methods; (2) satisfying Babuska-Brezzi condition methods. Convergence is established for each class of methods. Applications of the first class of methods to Stokes flow and compressible linear elasticity are presented. The second class of methods is applied to the Poisson, Timoshenko beam and incompressible elasticity problems. Numerical results demonstrate the good stability and accuracy of the methods, and confirm the error estimates.

• Research Organization: Stanford Univ., CA (USA)
• OSTI ID: 6584422
• Resource Relation: Other Information: Thesis (Ph. D.)
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
42 ENGINEERING
ELASTICITY
FINITE ELEMENT METHOD
GALERKIN-PETROV METHOD
LEAST SQUARE FIT
STOKES LAW
INTERPOLATION
VARIATIONAL METHODS
ITERATIVE METHODS
MAXIMUM-LIKELIHOOD FIT
MECHANICAL PROPERTIES
NUMERICAL SOLUTION
TENSILE PROPERTIES
657000* - Theoretical & Mathematical Physics
420400 - Engineering- Heat Transfer & Fluid Flow