On the Distribution of Errors in the Iterative Solution of a System of Linear Equations.
On the distribution of zeros of solutions of some types of differential equation
On the domain geometry dependence of the LBB condition
The LBB condition is well-known to guarantee the stability of a finite element (FE) velocity - pressure pair in incompressible flow calculations. To ensure the condition to be satisfied a certain constant should be positive and mesh-independent. The paper studies the dependence of the LBB condition on the domain geometry. For model domains such as strips and rings the substantial dependence of this constant on geometry aspect ratios is observed. In domains with highly anisotropic substructures...
On the double critical-state model for type-II superconductivity in 3D
In this paper we mathematically analyse an evolution variational inequality which formulates the double critical-state model for type-II superconductivity in 3D space and propose a finite element method to discretize the formulation. The double critical-state model originally proposed by Clem and Perez-Gonzalez is formulated as a model in 3D space which characterizes the nonlinear relation between the electric field, the electric current, the perpendicular component of the electric current...
On the economical solution method for a system of linear algebraic equations.
On the effect of numerical integration in the finite element solution of an elliptic problem with a nonlinear Newton boundary condition
This paper is concerned with the analysis of the finite element method for the numerical solution of an elliptic boundary value problem with a nonlinear Newton boundary condition in a two-dimensional polygonal domain. The weak solution loses regularity in a neighbourhood of boundary singularities, which may be at corners or at roots of the weak solution on edges. The main attention is paid to the study of error estimates. It turns out that the order of convergence is not dampened by the nonlinearity...
On the effect of temperature and velocity relaxation in two-phase flow models
We study a two-phase pipe flow model with relaxation terms in the momentum and energy equations, driving the model towards dynamic and thermal equilibrium. These equilibrium states are characterized by the velocities and temperatures being equal in each phase. For each of these relaxation processes, we consider the limits of zero and infinite relaxation times. By expanding on previously established results, we derive a formulation of the mixture sound velocity for the thermally relaxed model. This...
On the effect of temperature and velocity relaxation in two-phase flow models
We study a two-phase pipe flow model with relaxation terms in the momentum and energy equations, driving the model towards dynamic and thermal equilibrium. These equilibrium states are characterized by the velocities and temperatures being equal in each phase. For each of these relaxation processes, we consider the limits of zero and infinite relaxation times. By expanding on previously established results, we derive a formulation of the mixture sound velocity for the thermally relaxed model. This...
On the Effective Computation of the Inertia of a Non-Hermitian Matrix.
On the efficiency of adaptive MCMC algorithms.
On the efficiency of procedures for estimation of parameters in ARIMA models.
The paper discusses the implementation of the Newton-Raphson iterative method of estimation of parameters in the autoregressive integrated moving average (ARIMA) models. The efficiency of this method has been compared with other well known methods of estimation.
On the efficiency of some optimal quadrature formulas attached to some given quadrature formulas.
On the Efficient Solution of Nonlinear Finite Element Equations. II. Bound-Constrained Problems.
On the Efficient Solution of Nonlinear Finite Element Equations I.
On the efficient update of rectangular LU-factorizations subject to low rank modifications.
On the efficient use of the Galerkin-method to solve Fredholm integral equations
In the present paper we describe, how to use the Galerkin-method efficiently in solving boundary integral equations. In the first part we show how the elements of the system matrix can be computed in a reasonable time by using suitable coordinate transformations. These techniques can be applied to a wide class of integral equations (including hypersingular kernels) on piecewise smooth surfaces in 3-D, approximated by spline functions of arbitrary degree. In the second part we show, how to use the...
On the Eigenproblem for Convolution Integral Equations.
On the Eigenproblem for Normal Matrices.
On the Eigenvalue Distribution of a Class of Preconditioning Methods.
On the equivalence of primal and dual substructuring preconditioners.