Displaying similar documents to “The application of the thermal balance method for computation of warming in electric machines”

The box method and some error estimation

Mlýnek, Jaroslav

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This article focuses its attention on practical use of the box method for solving certain type of partial differential equations. The heat conduction problem of the oil transformer under stationary load is described by this equation. The knowledge of the transformer operating temperature is important for ensuring correct functionality and lifespan of transformer. We consider an elliptic partial differential equation of second order with the Newton boundary condition on a rectangular...

On the Newton-Kantorovich theorem and nonlinear finite element methods

Ioannis K. Argyros (2009)

Applicationes Mathematicae

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Using a weaker version of the Newton-Kantorovich theorem, we provide a discretization result to find finite element solutions of elliptic boundary value problems. Our hypotheses are weaker and under the same computational cost lead to finer estimates on the distances involved and a more precise information on the location of the solution than before.

On the effect of numerical integration in the finite element solution of an elliptic problem with a nonlinear Newton boundary condition

Ondřej Bartoš, Miloslav Feistauer, Filip Roskovec (2019)

Applications of Mathematics

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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...

A semi-smooth Newton method for solving elliptic equations with gradient constraints

Roland Griesse, Karl Kunisch (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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Semi-smooth Newton methods for elliptic equations with gradient constraints are investigated. The one- and multi-dimensional cases are treated separately. Numerical examples illustrate the approach and as well as structural features of the solution.

A comparison of some efficient numerical methods for a nonlinear elliptic problem

Balázs Kovács (2012)

Open Mathematics

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The aim of this paper is to compare and realize three efficient iterative methods, which have mesh independent convergence, and to propose some improvements for them. We look for the numerical solution of a nonlinear model problem using FEM discretization with gradient and Newton type methods. Three numerical methods have been carried out, namely, the gradient, Newton and quasi-Newton methods. We have solved the model problem with these methods, we have investigated the differences between...

Modeling and computation of heterogeneous implicit solvent and its applications for biomolecules

Duan Chen (2014)

Molecular Based Mathematical Biology

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Description of inhomogeneous dielectric properties of a solvent in the vicinity of ions has been attracting research interests in mathematical modeling for many years. From many experimental results, it has been concluded that the dielectric response of a solvent linearly depends on the ionic strength within a certain range. Based on this assumption, a new implicit solvent model is proposed in the form of total free energy functional and a quasi-linear Poisson-Boltzmann equation (QPBE)...