ON THE EXISTENCE AND STABILITY CONDITIONS FOR MIXED-HYBRID FINITE ELEMENT SOLUTIONS BASED ON REISSNER’S VARIATIONAL PRINCIPLE t
نویسندگان
چکیده
Abstract-The extensions of Reissner’s two-field (stress and displacement) principle to the cases wherein the displacement field is discontinuous and/or the stress field results in unreciprocated tractions, at a finite number of surfaces (“interelement boundaries”) in a domain (as, for instance, when the domain is discretized into finite elements), is considered. The conditions for the existence, uniqueness, and stability of mixed-hybrid finite element solutions based on such discontinuous fields, are summarized. The reduction of these global conditions to local (“element”) level, and the attendant conditions on the ranks of element matrices, are discussed. Two examples of stable, invariant, least-order elements -a .four-node square planar element and an eight-node cubic element-are discussed in detail.
منابع مشابه
Mathematical aspects of the general hybrid-mixed finite element methods and singular-value principle
In this paper the general hybrid-mixed ®nite element methods are investigated systematically in a framework of multi-®eld variational equations. The commonly accepted concept ``saddle point problem'' is argued in this paper. The existence, uniqueness, convergence, and stability properties of the solutions are proved undertaking the assumptions of Ker*-ellipticity and nested BBconditions. The re...
متن کاملWhitney Elements on Sparse Grids
The aim of this work is to generalize the idea of the discretizations on sparse grids to discrete differential forms. The extension to general l-forms in d dimensions includes the well known Whitney elements, as well as H(div; Ω)and H(curl; Ω)-conforming mixed finite elements. The formulation of Maxwell’s equations in terms of differential forms gives a crucial hint how they should be discretiz...
متن کاملNitsche’s method for parabolic partial differential equations with mixed time varying boundary conditions
We investigate a finite element approximation of an initial boundary value problem associated with parabolic Partial Differential Equations endowed with mixed time varying boundary conditions, switching from essential to natural and viceversa. The switching occurs both in time and in different portions of the boundary. For this problem, we apply and extend the Nitsche’s method presented in [Jun...
متن کاملA Note on the Existence and Uniqueness of Solutions of Frequency Domain Elastic Wave Problems: a Priori Estimates in H
In this note, we provide existence and uniqueness results for frequency domain elastic wave problems. These problems are posed on the complement of a bounded domain (the scatterer). The boundary condition at infinity is given by the Kupradze-Sommerfeld radiation condition and involves different Sommerfeld conditions on different components of the field. Our results are obtained by setting up th...
متن کاملStable variational approximations of boundary value problems for Willmore flow with Gaussian curvature
We study numerical approximations for geometric evolution equations arising as gradient flows for energy functionals that are quadratic in the principal curvatures of a two-dimensional surface. Beside the well-known Willmore and Helfrich flows we will also consider flows involving the Gaussian curvature of the surface. Boundary conditions for these flows are highly nonlinear, and we use a varia...
متن کامل