Displaying similar documents to “A numerical solution of a two-dimensional transport equation”

Application of relaxation scheme to degenerate variational inequalities

Jela Babušíková (2001)

Applications of Mathematics

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In this paper we are concerned with the solution of degenerate variational inequalities. To solve this problem numerically, we propose a numerical scheme which is based on the relaxation scheme using non-standard time discretization. The approximate solution on each time level is obtained in the iterative way by solving the corresponding elliptic variational inequalities. The convergence of the method is proved.

A comparison of the accuracy of the finite-difference solution to boundary value problems for the Helmholtz equation obtained by direct and iterative methods

Václav Červ, Karel Segeth (1982)

Aplikace matematiky

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The development of iterative methods for solving linear algebraic equations has brought the question of when the employment of these methods is more advantageous than the use of the direct ones. In the paper, a comparison of the direct and iterative methods is attempted. The methods are applied to solving a certain class of boundary-value problems for elliptic partial differential equations which are used for the numerical modeling of electromagnetic fields in geophysics. The numerical...

A numerical minimization scheme for the complex Helmholtz equation

Russell B. Richins, David C. Dobson (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

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We use the work of Milton, Seppecher, and Bouchitté on variational principles for waves in lossy media to formulate a finite element method for solving the complex Helmholtz equation that is based entirely on minimization. In particular, this method results in a finite element matrix that is symmetric positive-definite and therefore simple iterative descent methods and preconditioning can be used to solve the resulting system of equations. We also derive an error bound for the method...

Variational particle schemes for the porous medium equation and for the system of isentropic Euler equations

Michael Westdickenberg, Jon Wilkening (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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Both the porous medium equation and the system of isentropic Euler equations can be considered as steepest descents on suitable manifolds of probability measures in the framework of optimal transport theory. By discretizing these variational characterizations instead of the partial differential equations themselves, we obtain new schemes with remarkable stability properties. We show that they capture successfully the nonlinear features of the flows, such as shocks and rarefaction...