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1.
Summary This paper considers a fully practical piecewise linear finite element approximation of the Dirichlet problem for a second order self-adjoint elliptic equation,Au=f, in a smooth region< n (n=2 or 3) by the boundary penalty method. Using an unfitted mesh; that is h , an approximation of with dist (, h )Ch 2 is not in general a union of elements; and assuminguH 4 () we show that one can recover the total flux across a segment of the boundary of with an error ofO(h 2). We use these results to study a fully practical piecewise linear finite element approximation of an elliptic equation by the boundary penalty method when the prescribed data on part of the boundary is the total flux.Supported by a SERC research studentship  相似文献   

2.
Summary Finite element approximation of a nonlinear elliptic pseudomonotone second-order boundary value problem in a bounded nonpolygonal domain with mixed Dirichlet-Neumann boundary conditions is studied. In the discretization we approximate the domain by a polygonal one, use linear conforming triangular elements and evaluate integrals by numerical quadratures. We prove the solvability of the discrete problem and on the basis of compactness properties of the corresponding operator (which is not monotone in general) we prove the convergence of approximate solutions to an exact weak solutionuH 1 ). No additional assumption on the regularity of the exact solution is needed.  相似文献   

3.
A family of higher order mixed finite element methods for plane elasticity   总被引:8,自引:0,他引:8  
Summary The Dirichler problem for the equations of plane elasticity is approximated by a mixed finite element method using a new family of composite finite elements having properties analogous to those possessed by the Raviart-Thomas mixed finite elements for a scalar, second-order elliptic equation. Estimates of optimal order and minimal regularity are derived for the errors in the displacement vector and the stress tensor inL 2(), and optimal order negative norm estimates are obtained inH s () for a range ofs depending on the index of the finite element space. An optimal order estimate inL () for the displacement error is given. Also, a quasioptimal estimate is derived in an appropriate space. All estimates are valid uniformly with respect to the compressibility and apply in the incompressible case. The formulation of the elements is presented in detail.This work was performed while Professor Arnold was a NATO Postdoctoral Fellow  相似文献   

4.
Summary Let be a natural exponential family on and (V, ) be its variance function. Here, is the mean domain of andV, defined on , is the variance of . A problem of increasing interest in the literature is the following: Given an open interval and a functionV defined on , is the pair (V, ) a variance function of some natural exponential family? Here, we consider the case whereV is a polynomial. We develop a complex-analytic approach to this problem and provide necessary conditions for (V, ) to be such a variance function. These conditions are also sufficient for the class of third degree polynomials and certain subclasses of polynomials of higher degree.  相似文献   

5.
Summary We consider a functional J: W 10c 1,p (, X) ×B() [0, ], where X is a Banach space andB() the class of the Borel subsets of the open Rn, and we assume that J has a suitable semicontinuity property respect its first variable, and depends like a measure from the elements ofB(). We show that under certain conditions such a functional can be represented like a multiple integral of a Caratheodory integrand. The first paragraph is devoted to improve some classical results about Sobolev spaces W1,p(, R) in the case of W1,p(, X).  相似文献   

6.
Manfred Droste 《Order》1985,2(3):291-319
Using combinatorial and model-theoretic means, we examine the structure of normal subgroup lattices N(A()) of 2-transitive automorphism groups A() of infinite linearly ordered sets (, ). Certain natural sublattices of N(A()) are shown to be Stone algebras, and several first order properties of their dense and dually dense elements are characterized within the Dedekind-completion of (, ). As a consequence, A() has either precisely 5 or at least 221 (even maximal) normal subgroups, and various other group- and lattice-theoretic results follow.  相似文献   

7.
The problem of the construction in a bounded domain m with a Lipschitz boundary of a function H2(), for which the conormal derivative on coincides with the normal component of a given vector field u H1(,C 3), is discussed. The solution of this problem is given for piecewise smooth boundaries in the case m=3.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 163, pp. 17–28, 1987.  相似文献   

8.
We study the regularity of the minimizer u for the functional F (u,f)=|u|2 + |u–f{2 over all maps uH 1(, S 2). We prove that for some suitable functions f every minimizer u is smooth in if 0 and for the same functions f, u has singularities when is large enough.
Résumé On étudie la régularité des minimiseurs u du problème de minimisation minueH 1(,S2)(|u|2 + |u–f{2. On montre que pour certaines fonctions f, u est régulière lorsque 0 et pour les mêmes f, si est assez grand, alors u possède des singularités.
  相似文献   

9.
We consider measurable subsets {ofR}n with 0<m()<, and we assume that has a spectral set . (In the special case when is also assumed open, may be obtained as the joint spectrum of a family of commuting self-adjoint operators {H k: 1kn} in L 2 () such that each H k is an extension of i(/x k) on C c (), k=1, ..., n.)It is known that is a fundamental domain for a lattice if is itself a lattice. In this paper, we consider a class of examples where is not assumed to be a lattice. Instead is assumed to have a certain inhomogeneous form, and we prove a necessary and sufficient condition for to be a fundamental domain for some lattice in {ofR}n. We are thus able to decide the question, fundamental domain or not, by considering only properties of the spectrum . Our criterion is obtained as a corollary to a theorem concerning partitions of sets which have a spectrum of inhomogeneous form.Work supported in part by the NSF.Work supported in part by the NSRC, Denmark.  相似文献   

10.
We investigate the elastostatic deformation of a tube whose crosssection is a convex ring . The outer lateral surface is assumed to be held fixed and the inner surface is displaced in the axial direction a uniform distanceh. The problem becomes one of seeking minimizers for a functionalJ(u) = (|u|) dx whereu(x) is the axial displacement and(·) is nonconvex. When is an annulus minimizers are known to exist. We prove existence and nonexistence results by studying a relaxed problem obtained by replacing(|·|) with its lower convex envelope, **(|·|). If a minimizer forJ(·) exists it is also a solution to the relaxed problem and this leads to an overdetermined problem in some cases.WhenJ(·) has no minimizer, solutions of the relaxed problem are of interest. We show that the relaxed problem has a unique solution and give detailed information on its structure.This work was partially supported by National Science Foundation Grants DMS-8601515 and DMS-8704368.  相似文献   

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