256 research outputs found
Energy decay for solutions of the wave equation with general memory boundary conditions
We consider the wave equation in a smooth domain subject to Dirichlet
boundary conditions on one part of the boundary and dissipative boundary
conditions of memory-delay type on the remainder part of the boundary, where a
general borelian measure is involved. Under quite weak assumptions on this
measure, using the multiplier method and a standard integral inequality we show
the exponential stability of the system.
Some examples of measures satisfying our hypotheses are given, recovering and
extending some of the results from the literature.Comment: 14 pages, submitted to Diff. Int. Eq
A posteriori error estimates for a finite element approximation of transmission problems with sign changing coefficients
We perform the a posteriori error analysis of residual type of a transmission
problem with sign changing coefficients. According to [6] if the contrast is
large enough, the continuous problem can be transformed into a coercive one. We
further show that a similar property holds for the discrete problem for any
regular meshes, extending the framework from [6]. The reliability and
efficiency of the proposed estimator is confirmed by some numerical tests.Comment: 15 page
The BEM with graded meshes for the electric field integral equation on polyhedral surfaces
We consider the variational formulation of the electric field integral
equation on a Lipschitz polyhedral surface . We study the Galerkin
boundary element discretisations based on the lowest-order Raviart-Thomas
surface elements on a sequence of anisotropic meshes algebraically graded
towards the edges of . We establish quasi-optimal convergence of
Galerkin solutions under a mild restriction on the strength of grading. The key
ingredient of our convergence analysis are new componentwise stability
properties of the Raviart-Thomas interpolant on anisotropic elements
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