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Displaying 461 –
480 of
501
The paper studies mesh dependent numerical solution of groundwater problems with singularities, caused by boreholes represented as points, instead of a real radius. We show on examples, that the numerical solution of the borehole pumping problem with point source (singularity) can be related to the exact solution of a regular problem with adapted geometry of a finite borehole radius. The radius providing the fit is roughly proportional to the mesh step. Next we define a problem of fracture-rock...
We briefly discuss an abstract approximation framework and a convergence theory of parameter estimation for a general class of nonautonomous nonlinear evolution equations. A detailed discussion of the above theory has been given earlier by the authors in another paper. The application of this theory together with numerical results indicating the feasibility of this general least squares approach are presented in the context of quasilinear reaction diffusion equations.
The topic of this paper is the numerical analysis of time periodic solution for electro-magnetic phenomena. The Limit Absorption Method (LAM) which forms the basis of our study is presented. Theoretical results have been proved in the linear finite dimensional case. This method is applied to scattering problems and transport of charged particles.
The topic of this paper is the numerical analysis of time
periodic solution for electro-magnetic phenomena.
The Limit Absorption Method (LAM)
which forms the basis of our study is presented. Theoretical
results have been proved in the linear finite dimensional case. This
method is applied to scattering problems and transport of charged
particles.
In [Progress Math.233 (2005)], David suggested the existence of a new type of global minimizers for the Mumford-Shah functional in . The singular set of such a new minimizer belongs to a three parameters family of sets .
We first derive necessary conditions satisfied by global minimizers of this family. Then we are led to study the first eigenvectors of the Laplace-Beltrami operator with Neumann boundary conditions on subdomains of with three reentrant corners. The necessary conditions are...
Natural superconvergence of the least-squares finite element method is surveyed for the one- and two-dimensional Poisson equation. For two-dimensional problems, both the families of Lagrange elements and Raviart-Thomas elements have been considered on uniform triangular and rectangular meshes. Numerical experiments reveal that many superconvergence properties of the standard Galerkin method are preserved by the least-squares finite element method.
In this article we implement different numerical schemes to simulate the Schrödinger-Debye equations that occur in nonlinear optics. Since the existence of blow-up solutions is an open problem, we try to compute such solutions. The convergence of the methods is proved and simulations seem indeed to show that for at least small delays self-focusing solutions may exist.
In this article we implement different numerical schemes to simulate the
Schrödinger-Debye equations that occur in nonlinear optics. Since the
existence of blow-up solutions is an open problem, we try to compute such
solutions. The convergence of the methods is proved and simulations seem
indeed to show that for at least small delays self-focusing solutions may
exist.
A Markov process converging to a random state of the 6-vertex model is constructed. It is
used to show that a droplet of c-vertices is created in the antiferromagnetic phase and
that the shape of this droplet has four cusps.
We deal with numerical analysis and simulations of the Davey-Stewartson equations which model, for example, the evolution of water surface waves. This time dependent PDE system is particularly interesting as a generalization of the 1-d integrable NLS to 2 space dimensions. We use a time splitting spectral method where we give a convergence analysis for the semi-discrete version of the scheme. Numerical results are presented for various blow-up phenomena of the equation, including blowup of defocusing,...
We deal with numerical analysis and simulations of the Davey-Stewartson equations
which model, for example, the evolution of water surface waves.
This time dependent PDE system is particularly interesting as a generalization
of the 1-d integrable NLS to 2 space dimensions.
We use a time splitting spectral method where
we give a convergence analysis for the semi-discrete version of the scheme.
Numerical results are presented for various blow-up phenomena of
the equation, including blowup of defocusing,...
This work is devoted to the study of migraine with aura in the human brain. Following
[6], we class migraine as a propagation of a wave of depolarization through
the cells. The mathematical model used, based on a reaction-diffusion equation, is briefly
presented. The equation is considered in a duct containing a bend, in order to model one
of the numerous circumvolutions of the brain. For a wide set of parameters, one can
establish the existence...
The paper studies the convergence behavior of
Monte Carlo schemes for semiconductors.
A detailed analysis of the systematic error
with respect to numerical parameters is performed.
Different sources of systematic error are pointed out and
illustrated in a spatially one-dimensional test case.
The error with respect to the number of simulation particles
occurs during the calculation of the internal electric field.
The time step error, which is related to the splitting of transport and
electric field...
A sparse algebraic multigrid method is studied as a cheap and accurate way to compute approximations of Schur complements of matrices arising from the discretization of some symmetric and positive definite partial differential operators. The construction of such a multigrid is discussed and numerical experiments are used to verify the properties of the method.
A sparse algebraic multigrid method is studied as a cheap and accurate
way to compute approximations of Schur complements of matrices
arising from the discretization of some symmetric and positive definite
partial differential operators. The construction of such a multigrid is
discussed and numerical experiments are used to verify the properties
of the method.
The paper deals with the analysis and numerical study of the domain decomposition based preconditioner for algebraic systems arising from the discontinuous Galerkin (DG) discretization of the linear elliptic problems. We introduce the DG discretization of the model problem and present the spectral -bound of the corresponding linear algebraic systems. Moreover, we present the two-level additive Schwarz preconditioner together with the theoretical result related to the estimate of the condition number....
In this paper, we consider the blow-up solutions for a quasilinear parabolic partial differential equation . We numerically investigate the blow-up rates of these solutions by using a numerical method which is recently proposed by the authors [3].
Currently displaying 461 –
480 of
501