Search results for " Boundary"

Finite element approximations of the wave equation with Dirichlet boundary data defined on a bounded domain in R2

2006

Three solutions to mixed boundary value problem driven by p(z)-Laplace operator

2021

We prove the existence of at least three weak solutions to a mixed Dirichlet–Neumann boundary value problem for equations driven by the p(z)-Laplace operator in the principal part. Our approach is variational and use three critical points theorems.

Guaranteed error bounds for a class of Picard-Lindelöf iteration methods

2013

We present a new version of the Picard-Lindelof method for ordinary dif- ¨ ferential equations (ODEs) supplied with guaranteed and explicitly computable upper bounds of an approximation error. The upper bounds are based on the Ostrowski estimates and the Banach fixed point theorem for contractive operators. The estimates derived in the paper take into account interpolation and integration errors and, therefore, provide objective information on the accuracy of computed approximations. peerReviewed

Quasihyperbolic boundary conditions and Poincaré domains

2002

We prove that a domain in ${\Bbb R}^n$ whose quasihyperbolic metric satisfies a logarithmic growth condition with coefficient $\beta\le 1$ is a (q,p)-\Poincare domain for all p and q satisfying $p\in[1,\infty)\cap(n-n\beta,n)$ and $q\in[p,\beta p^*)$ , where $p^*=np/(n-p)$ denotes the Sobolev conjugate exponent. An elementary example shows that the given ranges for p and q are sharp. The proof makes use of estimates for a variational capacity. When p=2 we give an application to the solvability of the Neumann problem on domains with irregular boundaries. We also discuss the relationship between this growth condition on the quasihyperbolic metric and the s-John condition.

Energy localization in a nonlinear discrete system

1996

International audience; We show that, in the weak amplitude and slow time limits, the discrete equations describing the dynamics of a one-dimensional lattice can be reduced to a modified Ablowitz-Ladik equation. The stability of a continuous wave solution is then investigated without and with periodic boundary conditions; Energy localization via modulational instability is predicted. Our numerical simulations, performed on a cyclic system of six oscillators, agree with our theoretical predictions.

A regular variational boundary model for free vibrations of magneto-electro-elastic structures

2011

In this paper a regular variational boundary element formulation for dynamic analysis of two-dimensional magneto-electro-elastic domains is presented. The method is based on a hybrid variational principle expressed in terms of generalized magneto-electro-elastic variables. The domain variables are approximated by using a superposition of weighted regular fundamental solutions of the static magneto-electro-elastic problem, whereas the boundary variables are expressed in terms of nodal values. The variational principle coupled with the proposed discretization scheme leads to the calculation of frequency-independent and symmetric generalized stiffness and mass matrices. The generalized stiffne…

A Boundary/Interior Element Discretization Method for the Analysis of Two- and Three-Dimensional Elastic-Plastic Structures

1992

A coupled boundary/interior element method is presented for the analysis of elastic-plastic structures with material models endowed of dual internal variables. The domain field modelling is limited to the only plastic strains and strain-like internal variables, represented by their node values at a set of strain points in each interior element. The formulation, based on a Galerkin-type approach, is variationally consistent and leads to a fully symmetric-definite equation system. The backward difference method is adopted for the step-by-step integration procedure, and each step is addressed by an iterative predictor/corrector solution scheme. The analysis method is expected to be most approp…

Method of Lines and Finite Difference Schemes with Exact Spectrum for Solving Some Linear Problems of Mathematical Physics

2013

In this paper linear initial-boundary-value problems of mathematical physics with different type boundary conditions BCs and periodic boundary conditions PBCs are studied. The finite difference scheme FDS and the finite difference scheme with exact spectrum FDSES are used for the space discretization. The solution in the time is obtained analytically and numerically, using the method of lines and continuous and discrete Fourier methods.

Symmetric Galerkin Boundary Element Methods

1998

This review article concerns a methodology for solving numerically, for engineering purposes, boundary and initial-boundary value problems by a peculiar approach characterized by the following features: the continuous formulation is centered on integral equations based on the combined use of single-layer and double-layer sources, so that the integral operator turns out to be symmetric with respect to a suitable bilinear form. The discretization is performed either on a variational basis or by a Galerkin weighted residual procedure, the interpolation and weight functions being chosen so that the variables in the approximate formulation are generalized variables in Prager’s sense. As main con…

Deformation of melt-bearing systems—insight from in situ grain-scale analogue experiments

2005

Abstract The deformation behaviour of partially molten rocks was investigated using in situ analogue experiments with norcamphor+ethanol, as well as partially molten KNO 3 +LiNO 3 . Three general deformation regimes could be distinguished during bulk pure shear deformation. In regime I, above ca. 8–10 vol.% liquid (melt) fraction ( ϕ bulk ), deformation is by compaction, distributed granular flow, and grain boundary sliding (GBS). At ϕ bulk ϕ bulk (regime III), grains form a coherent framework that deforms by grain boundary migration accommodated dislocation creep, associated with efficient segregation of remaining liquid. The transition liquid fraction between regimes I and II ( ϕ LT ) dep…