Determination of the maximum temperature and its location is the matter of the greatest importance in many technological and scientific engineering applications. In terms of numerical calculations of the heat conduction equation by using uniform mesh increments in space, large computational cost is sometimes countered. However, adaptive grid refinement method could be computationally efficient ...

in this paper, a new numerical method for solving time-fractional diffusion equations is introduced. for this purpose, finite difference scheme for discretization in time and chebyshev collocation method is applied. also, to simplify application of the method, the matrix form of the suggested method is obtained. illustrative examples show that the proposed method is very efficient and accurate.

In this paper, we propose an efficient quadratic interpolation formula utilizing solution gradients computed and stored at nodes demonstrate its application to a third-order cell-centered finite-volume discretization on tetrahedral grids. The proposed is constructed based of computing projected derivative. It in that it completely eliminates the need compute store second derivatives variables o...

We derive a posteriori error estimates for the discretization of the heat equation in a unified and fully discrete setting comprising the discontinuous Galerkin, finite volume, mixed finite element, and conforming and nonconforming finite element methods in space and the backward Euler scheme in time. Our estimates are based on a H-conforming reconstruction of the potential, continuous and piec...

In this paper an evolving surface finite volume method is introduced for the numerical resolution of a transport diffusion problem on a family of moving hypersurfaces. These surfaces are assumed to evolve according to a given motion field. The ingredients of the method are an approximation of the family of surfaces by a family of interpolating simplicial meshes, where grid vertices move on moti...

1. Poisson Equation 1 2. Outline of Topics 3 2.1. Finite Difference Method 3 2.2. Finite Element Method 3 2.3. Finite Volume Method 3 2.4. Sobolev Spaces and Theory on Elliptic Equations 3 2.5. Iterative Methods: Conjugate Gradient and Multigrid Methods 3 2.6. Nonlinear Elliptic Equations 3 2.7. Fast Multiple Method 3 3. Physical Examples 4 3.1. Gauss’ law and Newtonian gravity 4 3.2. Electrost...

A numerical method for the reconstruction of interfaces in finite volume schemes for multiphase flows is presented. The computation of the triple-point at the intersection of three materials in two dimensions of space is addressed. The determination of the normal vectors between pairs of materials is obtained with a finite element approximation. A numerical method for the localization of a trip...

We present a hybrid finite-volume-particle numerical method for computing the transport of a passive pollutant by a flow. The flow is modeled by the oneand two-dimensional Saint-Venant system of shallow water equations and the pollutant propagation is described by a transport equation. This paper is an extension of our previous work [Chertock, Kurganov and Petrova, J. Sci. Comput. (to appear)],...