‎in this paper‎, ‎we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain‎. ‎this problem consists of determining the temperature on the interior boundary curve from the cauchy data (boundary temperature and heat flux) on the exterior boundary curve‎. ‎to this end‎, ‎the boundary integral equation method is used‎. ‎since the resulting system of linea...

In this paper, a high order compact difference scheme and a multigrid method are proposed for solving two-dimensional (2D) elliptic problems with variable coefficients and interior/boundary layers on nonuniform grids. Firstly, the original equation is transformed from the physical domain (with a nonuniform mesh) to the computational domain (with a uniform mesh) by using a coordinate transformat...

singular perturbation problems have been studied by many mathematicians. since the approximate solutions of these problems are as the sum of internal solution (boundary layer area) and external ones, the formation or non-formation of boundary layers should be specified. this paper, investigates this issue for a singular perturbation problem including a first order differential equation with gen...

in an earlier work we showed that for ordered fields f not isomorphic to the reals r, there are continuous 1-1 unctions on [0, 1]f which map some interior point to a boundary point of the image (and so are not open). here we show that over closed bounded intervals in the rationals q as well as in all non-archimedean ordered fields of countable cofinality, there are uniformly continuous 1-1 func...

Numerical solutions of convection–diffusion equations obtained using the Streamline–Upwind Petrov–Galerkin (SUPG) stabilisation typically possess spurious oscillations at layers. Spurious Oscillations at Layers Diminishing (SOLD) methods aim to suppress or at least diminish these oscillations without smearing the layers extensively. In the recent review by John and Knobloch (2007), numerical st...

In previous chapters boundary layers were evident as thin layers across which thermal, dynamic, and material properties of a free interior flow make a transition to their boundary values and/or boundary fluxes. In those cases the thinness of the boundary layer was typically a statement of the smallness of the relevant diffusivity; e.g., the depth h of the laminar Ekman boundary layer scales as ...

The wind driven aspects of the meridional overturning circulation of the world ocean and the Conveyor Belt is studied making use of a simple analytical model. The model consists of three reduced gravity layers with an inviscid Sverdrupian interior and a western boundary layer. The net north-south exchange is made possible by setting 5 appropriate western boundary conditions, so that most of the...