The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
We consider a degenerate parabolic system which models
the evolution of nematic liquid crystal with variable degree of orientation.
The system
is a slight modification
to that proposed in [Calderer et al., SIAM J. Math. Anal.33 (2002) 1033–1047], which is a special case of
Ericksen's general continuum model in [Ericksen, Arch. Ration. Mech. Anal.113 (1991) 97–120].
We prove the global existence
of weak solutions by passing to the limit in a regularized system.
Moreover, we
propose a practical...
We study a Lagrangian numerical scheme for solution of a nonlinear drift diffusion equation on an interval. The discretization is based on the equation’s gradient flow structure with respect to the Wasserstein distance. The scheme inherits various properties from the continuous flow, like entropy monotonicity, mass preservation, metric contraction and minimum/ maximum principles. As the main result, we give a proof of convergence in the limit of vanishing mesh size under a CFL-type condition. We...
A discontinuous Galerkin finite element method for an optimal
control problem related to semilinear parabolic PDE's is examined.
The schemes under consideration are discontinuous in time but
conforming in space. Convergence of discrete schemes of arbitrary
order is proven. In addition, the convergence of discontinuous
Galerkin approximations of the associated optimality system to the
solutions of the continuous optimality system is shown. The proof
is based on stability estimates at arbitrary time...
We formulate a finite element method for the computation of solutions to an anisotropic phase-field model for a binary alloy. Convergence is proved in the -norm. The convergence result holds for anisotropy below a certain threshold value. We present some numerical experiments verifying the theoretical results. For anisotropy below the threshold value we observe optimal order convergence, whereas in the case where the anisotropy is strong the numerical solution to the phase-field equation does not...
The problem of modeling acoustic waves scattered by an object with Neumann boundary condition is considered. The boundary condition is taken into account by means of the fictitious domain method, yielding a first order in time mixed variational formulation for the problem. The resulting system is discretized with two families of mixed finite elements that are compatible with mass lumping. We present numerical results illustrating that the Neumann boundary condition on the object is not always correctly...
The problem of modeling acoustic waves scattered by an object with
Neumann boundary condition is considered. The boundary condition is
taken into account by means of the fictitious domain method, yielding
a first order in time mixed variational formulation for the
problem. The resulting system is discretized
with two families of mixed finite elements that are compatible with
mass lumping. We present numerical results illustrating that the Neumann boundary condition on the object is not always...
We propose and analyse two convergent fully discrete schemes to solve the incompressible Navier-Stokes-Nernst-Planck-Poisson system.
The first scheme converges to weak solutions satisfying an energy and an entropy
dissipation law. The second scheme uses Chorin's
projection method to obtain an efficient approximation that converges to strong
solutions at optimal rates.
The incompressible MHD equations couple Navier-Stokes equations with Maxwell's equations
to describe the flow of a viscous, incompressible, and electrically conducting fluid in
a Lipschitz domain .
We verify convergence of iterates of different coupling and
decoupling fully discrete schemes towards weak solutions for
vanishing discretization parameters. Optimal first order of convergence is shown
in the presence of strong solutions for a splitting scheme which decouples
the computation of velocity...
We develop a method for counting number of cells and extraction of approximate cell centers in 2D and 3D images of early stages of the zebra-fish embryogenesis. The approximate cell centers give us the starting points for the subjective surface based cell segmentation. We move in the inner normal direction all level sets of nuclei and membranes images by a constant speed with slight regularization of this flow by the (mean) curvature. Such multi- scale evolutionary process is represented by a geometrical...
Currently displaying 21 –
33 of
33