Special issue: Editorial
Special issue: Editorial [Czech and Slovak Twin Seminar in Applied Mathematics 2006]
Special meshes and higher-order schemes for singularly perturbed boundary value problems.
Special Similarity Transformations in Connection with the Quadrant Interlocking Factorisation Techniques
Specifying and simulating complex models using Bassist.
Spectral analysis in connection with iterative solution of convection-diffusion equation.
Spectral approach for kernel-based interpolation
We describe how the resolution of a kernel-based interpolation problem can be associated with a spectral problem. An integral operator is defined from the embedding of the considered Hilbert subspace into an auxiliary Hilbert space of square-integrable functions. We finally obtain a spectral representation of the interpolating elements which allows their approximation by spectral truncation. As an illustration, we show how this approach can be used to enforce boundary conditions in kernel-based...
Spectral approximation for inner and outer solution of some SPP.
Spectral approximation of multiplication operators.
Spectral approximation of positive operators by iteration subspace method
The iteration subspace method for approximating a few points of the spectrum of a positive linear bounded operator is studied. The behaviour of eigenvalues and eigenvectors of the operators arising by this method and their dependence on the initial subspace are described. An application of the Schmidt orthogonalization process for approximate computation of eigenelements of operators is also considered.
Spectral Approximation of the Periodic-Nonperiodic Navier-Stokes Equations.
Spectral approximation of variationally formulated eigenvalue problems on curved domains.
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...
Spectral Galerkin approximation of Fokker-Planck equations with unbounded drift
This paper is concerned with the analysis and implementation of spectral Galerkin methods for a class of Fokker-Planck equations that arises from the kinetic theory of dilute polymers. A relevant feature of the class of equations under consideration from the viewpoint of mathematical analysis and numerical approximation is the presence of an unbounded drift coefficient, involving a smooth convex potential that is equal to along the boundary of the computational domain . Using a symmetrization...
Spectral Galerkin approximation of Fokker-Planck equations with unbounded drift
This paper is concerned with the analysis and implementation of spectral Galerkin methods for a class of Fokker-Planck equations that arises from the kinetic theory of dilute polymers. A relevant feature of the class of equations under consideration from the viewpoint of mathematical analysis and numerical approximation is the presence of an unbounded drift coefficient, involving a smooth convex potential U that is equal to +∞ along the boundary ∂D of the computational domain D. Using a symmetrization...
Spectral Methods for Exterior Elliptic Problems.
Spectral methods for one-dimensional kinetic models of granular flows and numerical quasi elastic limit
In this paper we introduce numerical schemes for a one-dimensional kinetic model of the Boltzmann equation with dissipative collisions and variable coefficient of restitution. In particular, we study the numerical passage of the Boltzmann equation with singular kernel to nonlinear friction equations in the so-called quasi elastic limit. To this aim we introduce a Fourier spectral method for the Boltzmann equation [25, 26] and show that the kernel modes that define the spectral method have the correct...