## Specification of monitor metrics for generating balanced numerical grids

Formulas of monitor metrics are introduced for generating the vector field-aligned and/or adaptive grids. Some results of numerical experiments are demonstrated.

## Numerical solution of 3D Navier-Stokes equations on staggered grids

One algorithm to solve the 3D mixed boundary value problem for the Navier-Stokes system of equations is presented in this paper. The 3D mixed finite volume exponential type approximations on staggered grids are used. To solve the resulting system, an algorithm based on a three-level iterative method is proposed. Results...

## On the finite volume approach to the 3D quasistructured grids

The finite volume methods and technologies for the solution of the 3D elliptic boundary value problems (BVPs), with a complex geometry, on the quasistrucured grids are proposed. The grid data structure and the element-by-element approach for computing the local balance and assembling the global matrices are considered. The results of...

## On the finite volume solution of the 1D parabolic nonlinear equation

On the finite volume solution of the 1D parabolic nonlinear equation

## On numerical experiments with some iterative solvers in mixed finite element method

This paper presents some numerical experiments with iterative solvers of algebraic linear systems for mixed finite element approximations.

## On monotone reconstruction of difference solution at isolated discontinuity

We propose a special monotone reconstruction algorithm in which the monotone property of a high order scheme is improved with the help of the monotone first order scheme. The algorithm provides spreading the shock only at one grid point and ensures second order of the integral convergence through the shock...

## On a massively parallel finite element method

This paper discusses the key-properties from the Parallel Finite Element Method (PFEM). It focuses at the PFEM applications in the context of non-conforming finite element basis functions (for maximal parallelism) on locally-bisection-refined tensor-product grids (for simple and cheap load balance techniques).

The Parallel Finite Element Method is an iterative solution...

## Mixed vector finite element method for solving first order system of Maxwell equations

This work is devoted to the construction and study of a computational scheme based on the mixed vector finite element method for modeling of the three-dimensional nonstationary electromagnetic fields. Numerical study of convergence of the mixed vector finite element method in the three-dimensional case on a class of problems, having...

## Comparative analysis of finite element approximation for the Navier-Stokes equations with basis functions of different orders

Finite element methods (the Uzawa algorithm and a mixed finite element method) for the solution of the Navier-Stokes equations on triangular grids are considered. For approximation of velocity and pressure, interpolating functions from different finite element spaces are chosen. The properties of the algorithms are tested on an analytical test...