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排序方式: 共有65条查询结果,搜索用时 15 毫秒
1.
G.N. Gatica 《Applied Mathematics Letters》1997,10(6):29-35
We study the solvability and Galerkin approximation of an exterior hyperelastic interface problem arising in plane elasticity. The weak formulation is obtained from an appropriate combination of a mixed finite element approach with a Dirichlet-to-Neumann method. The derivation of our results is based on some tools from nonlinear functional analysis and the Babuska-Brezzi theory for variational problems with constraints. 相似文献
2.
Gabriel N. Gatica Ernst P. Stephan 《Numerical Methods for Partial Differential Equations》2002,18(1):105-128
This article deals with an expanded mixed finite element formulation, based on the Hu‐Washizu principle, for a nonlinear incompressible material in the plane. We follow our related previous works and introduce both the stress and the strain tensors as further unknowns, which yields a two‐fold saddle point operator equation as the corresponding variational formulation. A slight generalization of the classical Babu?ka‐Brezzi's theory is applied to prove unique solvability of the continuous and discrete formulations, and to derive the corresponding a priori error analysis. An extension of the well‐known PEERS space is used to define an stable associated Galerkin scheme. Finally, we provide an a posteriori error analysis based on the classical Bank‐Weiser approach. © 2002 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 18: 105–128, 2002 相似文献
3.
In this paper we show that the quasi-symmetric coupling of finite and boundary elements of Bielak and MacCamy can be freed
of two very restricting hypotheses that appeared in the original paper: the coupling boundary can be taken polygonal/polyhedral
and coupling can be done using the normal stress instead of the pseudostress. We will do this by first considering a model
problem associated to the Yukawa equation, where we prove how compactness arguments can be avoided to show stability of Galerkin
discretizations of a coupled system in the style of Bielak–MacCamy’s. We also show how discretization properties are robust
in the continuation parameter that appears in the formulation. This analysis is carried out using a new and very simplified
proof of the ellipticity of the Johnson–Nédélec BEM–FEM coupling operator. Finally, we show how to apply the techniques that
we have fully developed in the model problem to the linear elasticity system. 相似文献
4.
José M. Gatica 《Applied Surface Science》2010,256(23):7111-7117
Coal-based honeycomb monoliths extruded using methods developed for ceramic materials have been used to retain methylene blue and p-nitrophenol from aqueous solutions. The influence of the filters’ thermal treatment on their textural properties and performance as adsorbents was examined. Characterization by N2 physisorption, mercury porosimetry and scanning electron microscopy along with adsorption tests under dynamic conditions suggest that, depending on the pollutant and its initial concentration, it can be more convenient to previously submit the monoliths to a simple carbonization or to an additional activation, with or without preoxidation, as a consequence of their different resulting pore structures. Infrared spectroscopy indicates that their different adsorption behaviour seems not to be related to differences in their surface chemical groups. In addition, axial crushing tests show that the monoliths have an acceptable mechanical resistance for the application investigated. 相似文献
5.
Taniguchi J Yamaguchi A Ishimoto H Ikegami H Matsushita T Wada N Gatica SM Cole MW Ancilotto F Inagaki S Fukushima Y 《Physical review letters》2005,94(6):065301
Heat capacity measurements have been made down to 5 mK for 3He fluid films adsorbed in one-dimensional (1D) nanometer-scale pores, 28 A in diameter, preplated with 4He of 1.47 atomic layers. At low 3He density, the heat capacity shows a density-dependent, Schottky-like peak near 150 mK asymptoting to the value corresponding to a 2D Boltzmann gas at high temperatures. The peak behavior is attributed to the crossover from a 2D gas to a 1D state at low temperatures. The degenerate state of the 1D 3He fluid is indicated by a predominantly linear temperature dependence below about 30 mK. 相似文献
6.
In this paper, we present a domain decomposition method, based on the general theory of Steklov-Poincaré operators, for a class of linear exterior boundary value problems arising in potential theory and heat conductivity. We first use a Dirichlet-to-Neumann mapping, derived from boundary integral equation methods, to transform the exterior problem into an equivalent mixed boundary value problem on a bounded domain. This domain is decomposed into a finite number of annular subregions, and the Dirichlet data on the interfaces is introduced as the unknown of the associated Steklov-Poincaré problem. This problem is solved with the Richardson method by introducing a Dirichlet-Robin-type preconditioner, which yields an iteration-by-subdomains algorithm well suited for parallel computations. The corresponding analysis for the finite element approximations and some numerical experiments are also provided. 相似文献
7.
Sergio Caucao Gabriel N. Gatica Ricardo Oyarzúa 《Numerical Methods for Partial Differential Equations》2019,35(1):295-324
In this article, we consider an augmented fully mixed variational formulation that has been recently proposed for the nonisothermal Oldroyd–Stokes problem, and develop an a posteriori error analysis for the 2‐D and 3‐D versions of the associated mixed finite element scheme. More precisely, we derive two reliable and efficient residual‐based a posteriori error estimators for this problem on arbitrary (convex or nonconvex) polygonal and polyhedral regions. The reliability of the proposed estimators draws mainly upon the uniform ellipticity of the bilinear forms of the continuous formulation, suitable assumptions on the domain and the data, stable Helmholtz decompositions, and the local approximation properties of the Clément and Raviart–Thomas operators. On the other hand, inverse inequalities, the localization technique based on bubble functions, and known results from previous works are the main tools yielding the efficiency estimate. Finally, several numerical results confirming the properties of the a posteriori error estimators and illustrating the performance of the associated adaptive algorithms are reported. 相似文献
8.
We deal with the iterative solution of linear systems arising from so-called dual-dual mixed finite element formulations. The linear systems are of a two-fold saddle point structure; they are indefinite and ill-conditioned. We define a special inner product that makes matrices of the two-fold saddle point structure, after a specific transformation, symmetric and positive definite. Therefore, the conjugate gradient method with this special inner product can be used as iterative solver. For a model problem, we propose a preconditioner which leads to a bounded number of CG-iterations. Numerical experiments for our model problem confirming the theoretical results are also reported.
9.
Summary This paper deals with an elliptic boundary value problem posed in the plane, with variable coefficients, but whose restriction to the exterior of a bounded domain reduces to a Helmholtz equation. We consider a mixed variational formulation in a bounded domain that contains the heterogeneous medium, coupled with a boundary integral method applied to the Helmholtz equation in . We utilize suitable auxiliary problems, duality arguments, and Fredholm alternative to show that the resulting formulation of the problem is well posed. Then, we define a corresponding Galerkin scheme by using rotated Raviart-Thomas subspaces and spectral elements (on the interface). We show that the discrete problem is uniquely solvable and convergent and prove optimal error estimates. Finally we illustrate our analysis with some results from computational experiments. 相似文献
10.
Gabriel R. Barrenechea Gabriel N. Gatica Jean-Marie Thomas 《Numerical Functional Analysis & Optimization》2013,34(1-2):7-32
We apply the boundary integral equation method and a primal mixed finite element approach to study the weak solvability and Galerkin approximations of linear interior transmission problems arising in potential theory and elastostatics. The existence and uniqueness of solution of the resulting weak formulations and of the associated discrete schemes are derived by using the classical theory for variational problems with constraints. Suitable finite element subspaces of Lagrange type satisfying the compatibility conditions are utilized for defining the Galerkin scheme. The error analysis and corresponding rates of convergence are also provided. 相似文献