We propose and analyze a combined finite volume–nonconforming finite element scheme on general meshes to simulate the two compressible phase flow in porous media. The diffusion term, which can be anisotropic and heterogeneous, is discretized by piecewise linear nonconforming triangular finite elements. The other terms are discretized by means of a cell-centered finite volume scheme on a dual me...

We consider a new fictitious domain approach of higher order accuracy. To implement Dirichlet conditions we apply the classical Nitsche method combined with a facet-based stabilization (ghost penalty). Both techniques are combined with a higher order isoparametric finite element space which is based on a special mesh transformation. The mesh transformation is build upon a higher order accurate ...

We consider a time-dependent and a steady linear convection-diffusion equation. These equations are approximately solved by a combined finite element – finite volume method: the diffusion term is discretized by Crouzeix-Raviart piecewise linear finite elements on a triangular grid, and the convection term by upwind barycentric finite volumes. In the unsteady case, the implicit Euler method is u...

Boundary value problems for elliptic second order equations in three-dimensional domains with piecewise smooth boundaries are considered. Discretization of the problem is performed using a conventional version of the nite element method with piecewise linear basis functions. The main purpose of the paper is the construction of a preconditioning operator for the resulting system of grid equation...

In this paper, piecewise-analytical and numerical solutions of singular perturbation initial-value problems are obtained by an adaptive multi-step differential transform method (MsDTM). The principle of the method is introduced, and then applied to different types of practical problems arising in science and engineering. Analytical and numerical solutions are obtained using piecewise convergent...

We consider the application of the piecewise monotonic data approximation method to some problems that are derived from univariate signal restoration. We present numerical examples in order to show the efficacy of a software package that implements the method in data fitting and in denoising data from a medical image. The piecewise monotonic approximation method makes the smallest change to the...

We analyse a streamline diiusion scheme on a special piecewise uniform mesh for a model time-dependent convection-diiusion problem. The method with piecewise linear elements is shown to be convergent, independently of the diiusion parameter, with a pointwise accuracy of almost order 5=4 outside the boundary layer and almost order 3=4 inside the boundary layer. Numerical results are also given.

By using the method of investigation of differential equations with piecewise constant argument and some integral inequalities of Gronwall type we obtain some results of asymptotic equivalence of the stable solutions of some differential equations with piecewise constant argument. Our results generalize and improve some recent results. AMS subject classifications: 34K25, 34K34

We consider initial/boundary value problems for the subdiffusion and diffusionwave equations involving a Caputo fractional derivative in time. We develop two fully discrete schemes based on the piecewise linear Galerkin finite element method in space and convolution quadrature in time with the generating function given by the backward Euler method/second-order backward difference method, and es...