In this paper, we propose a tailored-finite-point method for a type of linear singular perturbation problem in two dimensions. Our finite point method has been tailored to some particular properties of the problem. Therefore, our new method can achieve very high accuracy with very coarse mesh even for very small ε, i.e. the boundary layers and interior layers do not need to be resolved numerica...

in this manuscript, we study the inverse problem for non self-adjoint sturm--liouville operator $-d^2+q$ with eigenparameter dependent boundary and discontinuity conditions inside a finite closed interval. by defining  a new hilbert space and  using its spectral data of a kind, it is shown that the potential function can be uniquely determined by part of a set of values of eigenfunctions at som...

The flow in an enclosed rotating cylinder with a stationary lower end wall is investigated numerically. For fast rotation rates, the flow in the interior is primarily in the azimuthal direction, with an angular momentum distribution very close to that corresponding to solid-body rotation for about the inner-half radius. The differential rotation sets up a large-scale circulation that is primari...

Nanocrystalline materials show a higher strain-rate sensitivity in contrast to the conventional coarse-grained materials and a different grain size dependency. To explain these phenomenon, a finite element model is constructed that considers both grain interior and grain boundary deformation of nanocrystalline materials. The model consist of several crystalline cores with different orientations...

This paper analyzes the local properties of the symmetric interior penalty upwind discontinuous Galerkin method (SIPG) for the numerical solution of optimal control problems governed by linear reaction-advection-diffusion equations with distributed controls. The theoretical and numerical results presented in this paper show that for advection-dominated problems the convergence properties of the...

We think of the ocean as being driven by a variety of forces: tides, wind, surface buoyancy fluxes associated with heating, cooling, evaporation, precipitation and ice formation, and geothermal heating. Apart from tidal forces, which act throughout the ocean, geothermal plumes that rise far into the ocean interior, and locations of deep convection, these driving forces communicate their influen...

Time-dependent hydromagnetic phenomena in a rotating spherical cavity are investigated in the framework of an interior boundary-layer expansion. The interior problem is shown to contain waves whose frequencies are of order o, A o and A2u, where w is the rotation rate of the cavity and A2 = B2/4npu2R2 < 1 is the Alfven number. B is an imposed magnetic field, p the fluid density and R the radius ...