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Numerical flux-splitting for a class of hyperbolic systems with unilateral constraint

Florent Berthelin (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We study in this paper some numerical schemes for hyperbolic systems with unilateral constraint. In particular, we deal with the scalar case, the isentropic gas dynamics system and the full-gas dynamics system. We prove the convergence of the scheme to an entropy solution of the isentropic gas dynamics with unilateral constraint on the density and mass loss. We also study the non-trivial steady states of the system.

Numerical flux-splitting for a class of hyperbolic systems with unilateral constraint

Florent Berthelin (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We study in this paper some numerical schemes for hyperbolic systems with unilateral constraint. In particular, we deal with the scalar case, the isentropic gas dynamics system and the full-gas dynamics system. We prove the convergence of the scheme to an entropy solution of the isentropic gas dynamics with unilateral constraint on the density and mass loss. We also study the non-trivial steady states of the system.

Numerical solutions to integral equations equivalent to differential equations with fractional time

Bartosz Bandrowski, Anna Karczewska, Piotr Rozmej (2010)

International Journal of Applied Mathematics and Computer Science

This paper presents an approximate method of solving the fractional (in the time variable) equation which describes the processes lying between heat and wave behavior. The approximation consists in the application of a finite subspace of an infinite basis in the time variable (Galerkin method) and discretization in space variables. In the final step, a large-scale system of linear equations with a non-symmetric matrix is solved with the use of the iterative GMRES method.

Numerical studies of groundwater flow problems with a singularity

Hokr, Milan, Balvín, Aleš (2017)

Programs and Algorithms of Numerical Mathematics

The paper studies mesh dependent numerical solution of groundwater problems with singularities, caused by boreholes represented as points, instead of a real radius. We show on examples, that the numerical solution of the borehole pumping problem with point source (singularity) can be related to the exact solution of a regular problem with adapted geometry of a finite borehole radius. The radius providing the fit is roughly proportional to the mesh step. Next we define a problem of fracture-rock...

On a generalized Stokes problem

Václav Mácha (2011)

Open Mathematics

We deal with a generalization of the Stokes system. Instead of the Laplace operator, we consider a general elliptic operator and a pressure gradient with small perturbations. We investigate the existence and uniqueness of a solution as well its regularity properties. Two types of regularity are provided. Aside from the classical Hilbert regularity, we also prove the Hölder regularity for coefficients in VMO space.

On a phase-field model with a logarithmic nonlinearity

Alain Miranville (2012)

Applications of Mathematics

Our aim in this paper is to study the existence of solutions to a phase-field system based on the Maxwell-Cattaneo heat conduction law, with a logarithmic nonlinearity. In particular, we prove, in one and two space dimensions, the existence of a solution which is separated from the singularities of the nonlinear term.

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