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Implicit difference schemes for mixed problems related to parabolic functional differential equations

Milena Netka (2011)

Annales Polonici Mathematici

Solutions of initial boundary value problems for parabolic functional differential equations are approximated by solutions of implicit difference schemes. The existence and uniqueness of approximate solutions is proved. The proof of the stability is based on a comparison technique with nonlinear estimates of the Perron type for given operators. It is shown that the new methods are considerably better than the explicit difference schemes. Numerical examples are presented.

Implicit-explicit Runge–Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations

Erik Burman, Alexandre Ern (2012)

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

We analyze a two-stage implicit-explicit Runge–Kutta scheme for time discretization of advection-diffusion equations. Space discretization uses continuous, piecewise affine finite elements with interelement gradient jump penalty; discontinuous Galerkin methods can be considered as well. The advective and stabilization operators are treated explicitly, whereas the diffusion operator is treated implicitly. Our analysis hinges on L2-energy estimates on discrete functions in physical space. Our main...

Implicit-explicit Runge–Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations

Erik Burman, Alexandre Ern (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

We analyze a two-stage implicit-explicit Runge–Kutta scheme for time discretization of advection-diffusion equations. Space discretization uses continuous, piecewise affine finite elements with interelement gradient jump penalty; discontinuous Galerkin methods can be considered as well. The advective and stabilization operators are treated explicitly, whereas the diffusion operator is treated implicitly. Our analysis hinges on L2-energy estimates on discrete functions in physical space. Our main...

Implicit-explicit Runge–Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations

Erik Burman, Alexandre Ern (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

We analyze a two-stage implicit-explicit Runge–Kutta scheme for time discretization of advection-diffusion equations. Space discretization uses continuous, piecewise affine finite elements with interelement gradient jump penalty; discontinuous Galerkin methods can be considered as well. The advective and stabilization operators are treated explicitly, whereas the diffusion operator is treated implicitly. Our analysis hinges on L2-energy estimates on discrete functions in physical space. Our main...

Improved estimates for the Ginzburg-Landau equation : the elliptic case

Fabrice Bethuel, Giandomenico Orlandi, Didier Smets (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We derive estimates for various quantities which are of interest in the analysis of the Ginzburg-Landau equation, and which we bound in terms of the G L -energy E ε and the parameter ε . These estimates are local in nature, and in particular independent of any boundary condition. Most of them improve and extend earlier results on the subject.

Improved successive constraint method based a posteriori error estimate for reduced basis approximation of 2D Maxwell's problem

Yanlai Chen, Jan S. Hesthaven, Yvon Maday, Jerónimo Rodríguez (2009)

ESAIM: Mathematical Modelling and Numerical Analysis


In a posteriori error analysis of reduced basis approximations to affinely parametrized partial differential equations, the construction of lower bounds for the coercivity and inf-sup stability constants is essential. In [Huynh et al., C. R. Acad. Sci. Paris Ser. I Math.345 (2007) 473–478], the authors presented an efficient method, compatible with an off-line/on-line strategy, where the on-line computation is reduced to minimizing a linear functional under a few linear constraints. These constraints...

Improving Cancer Therapy by Doxorubicin and Granulocyte Colony-Stimulating Factor: Insights from a Computerized Model of Human Granulopoiesis

V. Vainstein, Y. Ginosar, M. Shoham, A. Ianovski, A. Rabinovich, Y. Kogan, V. Selitser, Z. Agur (2010)

Mathematical Modelling of Natural Phenomena

Neutropenia is a significant dose-limiting toxicity of cancer chemotherapy, especially in dose-intensified regimens. It is widely treated by injections of Granulocyte Colony-Stimulating Factor (G-CSF). However, optimal schedules of G-CSF administration are still not determined. In order to aid in identifying more efficacious and less neutropenic treatment protocols, we studied a detailed physiologically-based computer model of granulopoiesis, as affected by different treatment schedules of doxorubicin...

Impulsive Partial Hyperbolic Functional Differential Equations of Fractional Order with State-Dependent Delay

Abbas, Saïd, Benchohra, Mouffak (2010)

Fractional Calculus and Applied Analysis

MSC 2010: 26A33, 34A37, 34K37, 34K40, 35R11This paper deals with the existence and uniqueness of solutions of two classes of partial impulsive hyperbolic differential equations with fixed time impulses and state-dependent delay involving the Caputo fractional derivative. Our results are obtained upon suitable fixed point theorems.

In Memoriam Jindřich Nečas

Ivan Hlaváček, Oldřich John, Alois Kufner, Josef Málek, Nečasová, Š. , Jana Stará, Vladimír Šverák (2004)

Mathematica Bohemica

Incompressible inviscid limit for the full magnetohydrodynamic flows on expanding domains

Young-Sam Kwon (2020)

Applications of Mathematics

In this paper we study the incompressible inviscid limit of the full magnetohydrodynamic flows on expanding domains with general initial data. By applying the relative energy method and carrying out detailed analysis on the oscillation part of the velocity, we prove rigorously that the gradient part of the weak solutions of the full magnetohydrodynamic flows converges to the strong solution of the incompressible Euler system in the whole space, as the Mach number, viscosity as well as the heat conductivity...

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