This work presents a new analytical method to transform exact solutions of linear diffusion equations into exact ones for nonlinear advection-diffusion models. The proposed formulation, based on Bäcklund transformations, is employed to obtain velocity fields for the unsteady two-dimensional Helmholtz equation, starting from analytical solutions of a heat conduction type model.

We prove the existence of an infinite discrete set of transmission eigenvalues corresponding to the scattering problem for isotropic and anisotropic inhomogeneous media for both the Helmholtz and Maxwell’s equations. Our discussion includes the case of the interior transmission problem for an inhomogeneous medium with cavities, i.e. subregions with contrast zero.

This paper presents an optimal nonconforming adaptive finite element algorithm and proves its quasi-optimal complexity for the Stokes equations with respect to natural approximation classes. The proof does not explicitly involve the pressure variable and follows from a novel discrete Helmholtz decomposition of deviatoric functions. Mathematics Subject Classification (2000) Primary 65N12 · 65N15...

We construct Schwarz domain decomposition preconditioners for plane wave discontinuous Galerkin methods for Helmholtz boundary value problems. In particular, we consider additive and multiplicative non-overlapping Schwarz methods. Numerical tests show good performance of these preconditioners when solving the linear system of equations with GMRES.

Background: Effects of electromagnetic fields on healing have been investigated for centuries. Substantial data indicates that exposure to electromagnetic field can lead to enhanced healing in both soft and hard tissues. Helmholtz coil is a device that generates pulsed electromagnetic fields. Objective: In this study, a pair of Helmholtz coils for enhancing thehealing process in periodontitis w...

We derive uniform weighted L 2 and Morrey-Campanato type estimates for Helmholtz Equations in a medium with a variable index which is not necessarily constant at innnity. Our technique is based on a multiplier method with appropriate weights which generalize those of Morawetz for the wave equation. We also extend our method to the wave equation.

We study a model initially proposed to describe a mixture of (CO) 1−x (N 2) x adsorbed on exfoliated graphite. The approach used here is that of mean field theory. The Mean Field equations and the Helmholtz Free Energy are found. Phase diagrams are calculated too, and it is possible to find an analytic expression for the second order phase transition line.

This paper deals with the a posteriori error analysis of mixed finite element methods for second order elliptic equations. It is shown that a reliable and efficient error estimator can be constructed using a postprocessed solution of the method. The analysis is performed in two different ways: under a saturation assumption and using a Helmholtz decomposition for vector fields.

This paper present the analogous of the Helmholtz conditions for first and second order difference equations systems. We obtain variational implicit algoritms used in numerical analysis and numerical integration schemes for Hamilton systems. We give some representative examples. Mathematics Subject Classification: 70H05, 39A12