Spectral and related properties about the Emden-Fowler equation -...u = ...e... on circular domains.
Spectral and scattering theory for symbolic potentials of order zero
Spectral and scattering theory for the Schrödinger operator with strongly oscillating potentials
Spectral and scattering theory in deformed optical wave guides.
Spectral Approximation of the Periodic-Nonperiodic Navier-Stokes Equations.
Spectral approximation of variationally formulated eigenvalue problems on curved domains.
Spectral Asymmetrie and Zeta Functions.
Spectral asymptotics and bifurcation for nonlinear multiparameter elliptic eigenvalue problems.
Spectral asymptotics for Hill's equation near the potential maximum
Spectral asymptotics for manifolds with cylindrical ends
The spectrum of the Laplacian on manifolds with cylindrical ends consists of continuous spectrum of locally finite multiplicity and embedded eigenvalues. We prove a Weyl-type asymptotic formula for the sum of the number of embedded eigenvalues and the scattering phase. In particular, we obtain the optimal upper bound on the number of embedded eigenvalues less than or equal to , where is the dimension of the manifold.
Spectral asymptotics for multi-quasi-elliptic operators in
Spectral asymptotics for Schrödinger operators with a degenerate potential
Spectral Asymptotics for the -Neumann Problem
Spectral asymptotics of Laplace operators on surfaces with cusps.
Spectral convergence of the discrete Laplacian on models of a metrized graph.
Spectral decomposition of Green’s integrals and existence of -solutions of matrix factorizations of the Laplace operator in a ball
Spectral discretization of Darcy equations coupled with Navier-Stokes equations by vorticity-velocity-pressure formulation
We consider a model coupling the Darcy equations in a porous medium with the Navier-Stokes equations in the cracks, for which the coupling is provided by the pressure's continuity on the interface. We discretize the coupled problem by the spectral element method combined with a nonoverlapping domain decomposition method. We prove the existence of solution for the discrete problem and establish an error estimation. We conclude with some numerical tests confirming the results of our analysis.
Spectral element discretization of the heat equation with variable diffusion coefficient
We are interested in the discretization of the heat equation with a diffusion coefficient depending on the space and time variables. The discretization relies on a spectral element method with respect to the space variables and Euler's implicit scheme with respect to the time variable. A detailed numerical analysis leads to optimal a priori error estimates.
Spectral element discretization of the vorticity, velocity and pressure formulation of the Stokes problem
We consider the Stokes problem provided with non standard boundary conditions which involve the normal component of the velocity and the tangential components of the vorticity. We write a variational formulation of this problem with three independent unknowns: the vorticity, the velocity and the pressure. Next we propose a discretization by spectral element methods which relies on this formulation. A detailed numerical analysis leads to optimal error estimates for the three unknowns and numerical...
Spectral element discretization of the vorticity, velocity and pressure formulation of the Stokes problem
We consider the Stokes problem provided with non standard boundary conditions which involve the normal component of the velocity and the tangential components of the vorticity. We write a variational formulation of this problem with three independent unknowns: the vorticity, the velocity and the pressure. Next we propose a discretization by spectral element methods which relies on this formulation. A detailed numerical analysis leads to optimal error estimates for the three unknowns and numerical...