Implicit second order partial differential equations
Implicit-explicit Runge–Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations
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
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
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 Difference Schemes for the Dirichlet Problem of Poisson's Equation in the Neighbourhood of Corners.
Improved estimates for the Ginzburg-Landau equation : the elliptic case
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 -energy and the parameter . 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 K-K algorithm for computing Lyapunov values
Improved least-squares error estimates for scalar hyperbolic problems.
Improved successive constraint method based a posteriori error estimate for reduced basis approximation of 2D Maxwell's problem
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...
Improved theory for a nonlinear degenerate parabolic equation
Improving Cancer Therapy by Doxorubicin and Granulocyte Colony-Stimulating Factor: Insights from a Computerized Model of Human Granulopoiesis
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 nonlocal nonlinear parabolic differential problems.
Impulsive Partial Hyperbolic Functional Differential Equations of Fractional Order with State-Dependent Delay
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.
Impuretés dans une structure périodique
In Memoriam Jindřich Nečas
Inclusions de Sobolev en calcul de Weyl-Hörmander et champs de vecteurs sous-elliptiques
Incompressible flows of an ideal fluid with vorticity in borderline spaces of Besov type
Incompressible inviscid limit for the full magnetohydrodynamic flows on expanding domains
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...
Incompressible, inviscid limit of the compressible Navier–Stokes system
Incompressible limit of a fluid-particle interaction model
The incompressible limit of the weak solutions to a fluid-particle interaction model is studied in this paper. By using the relative entropy method and refined energy analysis, we show that, for well-prepared initial data, the weak solutions of the compressible fluid-particle interaction model converge to the strong solution of the incompressible Navier-Stokes equations as long as the Mach number goes to zero. Furthermore, the desired convergence rates are also obtained.