In this paper a method is presented in details to solve a nonlinear partial differential equation which has many applications in engineering fields. The boundary condition is mixed to be able to define the value of function on its variation on the boundary. Examples are given to demonstrate the accuracy and efficiency of the method.

the determination of an unknown boundary condition, in a nonlinaer inverse diffusion problem is considered. for solving these ill-posed inverse problems, galerkin method based on sinc basis functions for space and time will be used. to solve the system of linear equation, a noise is imposed and tikhonove regularization is applied. by using a sensor located at a point in the domain of $x$, say $...

In this paper, implementation of an extended form of a no-slip wall boundary condition is presented for the three-dimensional (3-D) lattice Boltzmann method (LBM) for solving the incompressible fluid flows with complex geometries. The boundary condition is based on the off-lattice scheme with a polynomial interpolation which is used to reconstruct the curved or irregular wall boundary on the ne...

We consider the homogenization of the Navier-Stokes equation, set in a channel with a rough boundary, of small amplitude and wavelength ǫ. It was shown recently that, for any non-degenerate roughness pattern, and for any reasonable condition imposed at the rough boundary, the homogenized boundary condition in the limit ε = 0 is always no-slip. We give in this paper error estimates for this homo...

This paper poses two magnetostatic problems in cylindrical coordinates with different permeabilities for each region. In the first problem the boundary condition of the second kind is used while in the second one, the boundary condition of the third kind is utilized. These problems are solved using the finite element and finite difference methods. In second problem, the results of the finite di...