An incomplete-factorization preconditioning using repeated red-black ordering.
An integral equation technique for solving mixed boundary value problems
An inverse eigenvalue problem for an arbitrary multiply connected bounded region: An extension to higher dimensions.
An inverse Neumann problem.
An inverse problem for a general annular drum with positive smooth functions in the Robin boundary conditions.
An inverse problem for a general doubly-connected bounded domain with impedance boundary conditions.
An inverse problem for Helmholtz's equation.
An inverse problem for the equation
Let be a bounded, convex planar domain whose boundary has a not too degenerate curvature. In this paper we provide partial answers to an identification question associated with the boundary value problemWe prove two results: 1) If is not a ball and if one considers only solutions with , then there exist at most finitely many pairs of coefficients so that the normal derivative equals a given .2) If one imposes no sign condition on the solutions but one additionally supposes that is sufficiently...
An estimate and a superconvergence result for a Galerkin method for elliptic equations based on tensor products of piecewise polynomials
An overdetermined elliptic problem in a domain with countably rectifiable boundary
We examine an elliptic equation in a domain Ω whose boundary ∂Ω is countably (m-1)-rectifiable. We also assume that ∂Ω satisfies a geometrical condition. We are interested in an overdetermined boundary value problem (examined by Serrin [Arch. Ration. Mech. Anal. 43 (1971)] for classical solutions on domains with smooth boundary). We show that existence of a solution of this problem implies that Ω is an m-dimensional Euclidean ball.
Analytic properties of the resolvent for the Helmholtz operator outside a periodic surface
Anisotropic mesh refinement in polyhedral domains: error estimates with data in L2(Ω)
The paper is concerned with the finite element solution of the Poisson equation with homogeneous Dirichlet boundary condition in a three-dimensional domain. Anisotropic, graded meshes from a former paper are reused for dealing with the singular behaviour of the solution in the vicinity of the non-smooth parts of the boundary. The discretization error is analyzed for the piecewise linear approximation in the H1(Ω)- and L2(Ω)-norms by using a new quasi-interpolation operator. This new interpolant...
Aposteriorní odhady chyby v metodě konečných prvků
Application of the -expansion method for the Burgers, Fisher and Burgers–Fisher equations.
Approximation by Finite Differences of the Propagation of Acoustic Waves in Stratified Media.
Approximation by generalized impedance boundary conditions of a transmission problem in acoustic scattering
This paper addresses some results on the development of an approximate method for computing the acoustic field scattered by a three-dimensional penetrable object immersed into an incompressible fluid. The basic idea of the method consists in using on-surface differential operators that locally reproduce the interior propagation phenomenon. This approach leads to integral equation formulations with a reduced computational cost compared to standard integral formulations coupling both the transmitted...
Approximation by generalized impedance boundary conditions of a transmission problem in acoustic scattering
This paper addresses some results on the development of an approximate method for computing the acoustic field scattered by a three-dimensional penetrable object immersed into an incompressible fluid. The basic idea of the method consists in using on-surface differential operators that locally reproduce the interior propagation phenomenon. This approach leads to integral equation formulations with a reduced computational cost compared to standard integral formulations coupling both the transmitted...
Approximation of a degenerated elliptic boundary value problem by a finite element method
Aproximación de un problema elíptico singular mediante elementos finitos isoparamétricos degenerados.
Asymptotic analysis of an approximate model for time harmonic waves in media with thin slots
In this article, we derive a complete mathematical analysis of a coupled 1D-2D model for 2D wave propagation in media including thin slots. Our error estimates are illustrated by numerical results.