The Existence of Finite Element Minimizers
نویسنده
چکیده
We present a general theorem on the existence of nite element minimizers for the approximation of variational problems of multiple inte-grals. Our theorem applies to variational problems for which a minimum does not exist in innnite-dimensional spaces of functions. Such problems occur in models for microstructure in martensitic and ferromagnetic crystals .
منابع مشابه
A new positive definite semi-discrete mixed finite element solution for parabolic equations
In this paper, a positive definite semi-discrete mixed finite element method was presented for two-dimensional parabolic equations. In the new positive definite systems, the gradient equation and flux equations were separated from their scalar unknown equations. Also, the existence and uniqueness of the semi-discrete mixed finite element solutions were proven. Error estimates were also obtaine...
متن کاملhp-Spectral Finite Element Analysis of Shear Deformable Beams and Plates
There are different finite element models in place for predicting the bending behavior of shear deformable beams and plates. Mostly, the literature abounds with traditional equi-spaced Langrange based low order finite element approximations using displacement formulations. However, the finite element models of Timoshenko beams and Mindlin plates with linear interpolation of all generalized disp...
متن کاملComposition of resolvents and quasi-nonexpansive multivalued mappings in Hadamared spaces
The proximal point algorithm, which is a well-known tool for finding minima of convex functions, is generalized from the classical Hilbert space framework into a nonlinear setting, namely, geodesic metric spaces of nonpositive curvature. In this paper we propose an iterative algorithm for finding the common element of the minimizers of a finite family of convex functions a...
متن کاملNonlinear Finite Element Analysis of Thermoelastic Stresses of FGM Rotating Disk Considering Temperature-Dependency of Material Properties
In the present paper, nonlinear radial and hoop thermoelastic stresses analysis of a disk made of FGMs material is investigated. According to this purpose, finite element method is used. In the present method, second-order one-dimensional element (with three node points) is proposed. The geometrical and stress boundary conditions are defined in the state of non-existence of external pressure an...
متن کاملNumerical Methods for Minimizers and Microstructures in Nonlinear Elasticity
A standard finite element method and a finite element truncation method are applied to solve the boundary value problems of nonlinear elasticity with certain nonconvex stored energy functions such as those of St. Venant-Kirchhoff materials. Finite element solutions are proved to exist and to be in the form of minimizers in appropriate sets of admissible finite element functions for both methods...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1997