Éléments finis et problèmes elliptiques dégénérés
Enthalpy model for heating, melting, and vaporization in laser ablation.
Exact, approximate solutions and error bounds for coupled implicit systems of partial differential equations.
Existence and Approximation of Solutions of Non-Linear Elliptic Equations.
Existenzsätze mit der Linienmethode für Parabolische Probleme und periodische Lösungen von ut = f(t,x,u,ux,uxx).
Extrapolation Methods for Dynamic Partial Differential Equations.
Galerkin method operator differential equations with Lipschitz continuous coefficients
Iterative solving of partial differential equations
-error estimates for variational inequalities with Hölder continuous obstacle
Lösung der Dirichletproblems und Konvergenz der Differenzenapproximation für elliptische Differentialgleichungen zweiter Ordnung.
Methane hydrate formation and decomposition.
Minimizing Oseen-Frank energy for nematic liquid crystals : algorithms and numerical results
Multiphoton response of retinal rod photoreceptors.
Nonobtuse Triangulation of Polygons.
Nonreflecting Boundary Conditions for Hyperbolic Conservation laws
Numerical approach to a rate-independent model of decohesion in laminated composites
In this paper, we present a numerical approach to evolution of decohesion in laminated composites based on incremental variational problems. An energy-based framework is adopted, in which we characterize the system by the stored energy and dissipation functionals quantifying reversible and irreversible processes, respectively. The time-discrete evolution then follows from a solution of incremental minimization problems, which are converted to a fully discrete form by employing the conforming finite...
Numerical Approximations of the Dynamical System Generated by Burgers’ Equation with Neumann–Dirichlet Boundary Conditions
Using Burgers’ equation with mixed Neumann–Dirichlet boundary conditions, we highlight a problem that can arise in the numerical approximation of nonlinear dynamical systems on computers with a finite precision floating point number system. We describe the dynamical system generated by Burgers’ equation with mixed boundary conditions, summarize some of its properties and analyze the equilibrium states for finite dimensional dynamical systems that are generated by numerical approximations of this...
Numerical aspects of the nonlinear Schrödinger equation in the semiclassical limit in a supercritical regime
We study numerically the semiclassical limit for the nonlinear Schrödinger equation thanks to a modification of the Madelung transform due to Grenier. This approach allows for the presence of vacuum. Even if the mesh size and the time step do not depend on the Planck constant, we recover the position and current densities in the semiclassical limit, with a numerical rate of convergence in accordance with the theoretical results, before shocks appear in the limiting Euler equation. By using simple...
Numerical aspects of the nonlinear Schrödinger equation in the semiclassical limit in a supercritical regime
We study numerically the semiclassical limit for the nonlinear Schrödinger equation thanks to a modification of the Madelung transform due to Grenier. This approach allows for the presence of vacuum. Even if the mesh size and the time step do not depend on the Planck constant, we recover the position and current densities in the semiclassical limit, with a numerical rate of convergence in accordance with the theoretical results, before shocks appear in the limiting Euler equation. By using simple...
Numerical solution of several models of internal transonic flow
The paper deals with numerical solution of internal flow problems. It mentions a long tradition of mathematical modeling of internal flow, especially transonic flow at our department. Several models of flow based on potential equation, Euler equations, Navier-Stokes and Reynolds averaged Navier-Stokes equations with proper closure are considered. Some mathematical and numerical properties of the model are mentioned and numerical results achieved by in-house developed methods are presented.