An Extrerior Mixed Boundary Value Problem for the Helmholtz Equation
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.