Equivalence of Finite Element Methods for Problems in Elasticity
نویسندگان
چکیده
منابع مشابه
Finite Element Methods for Linear Elasticity
Conditions for Stable Approximation Schemes Basic idea: Mimic structure of continuous problem. To establish stability of continuous problem, only used last two spaces in top sequence and last three spaces in bottom sequence. Λn−1(K) dn−1 −−−→ Λn(K)→ 0 ↗ Sn−2 ↗ Sn−1 Λn−2(V) dn−2 −−−→ Λn−1(V) dn−1 −−−→ Λn(V)→ 0. Thus, look for five finite dimensional spaces connected by a similar structure, i.e.,...
متن کاملFinite Element Methods for a Class of Nonlinear Boundary - Value Problems in Finite Elasticity
I So'U ds, anz where n is an open bounded domain in mn, n = 1, 2, or 3, Po = PO(x) is the mass density of a particle x € n in the reference configuration of the body, o(u) is the strain energy function, f is the applied body force density, So is an applied traction on a portion an? of the boundary an of n where an = anI U aoz and, for convenlence, we set u = 0 a.e. on anI' The functional TI is ...
متن کاملAdaptive Finite Element Methods for Multiphysics Problems Adaptive Finite Element Methods for Multiphysics Problems
In this thesis we develop and evaluate the performance of adaptive finite element methods for multiphysics problems. In particular, we propose a methodology for deriving computable error estimates when solving unidirectionally coupled multiphysics problems using segregated finite element solvers. The error estimates are of a posteriori type and are derived using the standard framework of dual w...
متن کاملNonconforming Finite Element Methods for the Equations of Linear Elasticity
In the adaptation of nonconforming finite element methods to the equations of elasticity with traction boundary conditions, the main difficulty in the analysis is to prove that an appropriate discrete version of Korn's second inequality is valid. Such a result is shown to hold for nonconforming piecewise quadratic and cubic finite elements and to be false for nonconforming piecewise linears. Op...
متن کاملAdaptive Finite Element Methods for Parameter Estimation Problems in Linear Elasticity
In this paper, the Lamé coefficients in the linear elasticity problem are estimated by using the measurements of displacement. Some a posteriori error estimators for the approximation error of the parameters are derived, and then adaptive finite element schemes are developed for the discretization of the parameter estimation problem, based on the error estimators. The GaussNewton method is empl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 1990
ISSN: 0036-1429,1095-7170
DOI: 10.1137/0727086