Analysis of parabolic difference schemes by Gerschgorin's method
Analysis of patch substructuring methods
Patch substructuring methods are non-overlapping domain decomposition methods like classical substructuring methods, but they use information from geometric patches reaching into neighboring subdomains condensated, on the interfaces to enhance the performance of the method, while keeping it non-overlapping. These methods are very convenient to use in practice, but their convergence properties have not been studied yet. We analyze geometric patch substructuring methods for the special case of one...
Analysis of pattern formation using numerical continuation
The paper deals with the issue of self-organization in applied sciences. It is particularly related to the emergence of Turing patterns. The goal is to analyze the domain size driven instability: We introduce the parameter , which scales the size of the domain. We investigate a particular reaction-diffusion model in 1-D for two species. We consider and analyze the steady-state solution. We want to compute the solution branches by numerical continuation. The model in question has certain symmetries....
Analysis of second order differential operators on Heisenberg groups. I.
Analysis of second order differential operators with complex coefficients on the Heisenberg group.
Analysis of Synchronization in a Neural Population by a Population Density Approach
In this paper we deal with a model describing the evolution in time of the density of a neural population in a state space, where the state is given by Izhikevich’s two - dimensional single neuron model. The main goal is to mathematically describe the occurrence of a significant phenomenon observed in neurons populations, the synchronization. To this end, we are making the transition to phase density population, and use Malkin theorem to calculate...
Analysis of Thacker's method for solving the linearized shallow water equations
Analysis of the accuracy and convergence of equation-free projection to a slow manifold
In [C.W. Gear, T.J. Kaper, I.G. Kevrekidis and A. Zagaris, SIAM J. Appl. Dyn. Syst. 4 (2005) 711–732], we developed a class of iterative algorithms within the context of equation-free methods to approximate low-dimensional, attracting, slow manifolds in systems of differential equations with multiple time scales. For user-specified values of a finite number of the observables, the mth member of the class of algorithms () finds iteratively an approximation of the appropriate zero of the (m+1)st...
Analysis of the boundary symbol for the two-phase Navier-Stokes equations with surface tension
The two-phase free boundary value problem for the Navier-Stokes system is considered in a situation where the initial interface is close to a halfplane. We extract the boundary symbol which is crucial for the dynamics of the free boundary and present an analysis of this symbol. Of particular interest are its singularities and zeros which lead to refined mapping properties of the corresponding operator.
Analysis of the DGFEM for nonlinear convection-diffusion problems.
Analysis of the Du Fort-Frankel method for linear systems
Analysis of the finite element method for transmission/mixed boundary value problems on general polygonal domains.
Analysis of the flows of incompressible fluids with pressure dependent viscosity fulfilling as
Over a large range of the pressure, one cannot ignore the fact that the viscosity grows significantly (even exponentially) with increasing pressure. This paper concerns long-time and large-data existence results for a generalization of the Navier-Stokes fluid whose viscosity depends on the shear rate and the pressure. The novelty of this result stems from the fact that we allow the viscosity to be an unbounded function of pressure as it becomes infinite. In order to include a large class of viscosities...
Analysis of the free boundary for the p-parabolic variational problem (p ≥ 2).
Abstract Variational inequalities (free boundaries), governed by the p-parabolic equation (p > 2), are the objects of investigation in this paper. Using intrinsic scaling we establish the behavior of solutions near the free boundary. A consequence of this is that the time levels of the free boundary are porous (in N-dimension) and therefore its Hausdorff dimension is less than N. In particular the N-Lebesgue measure of the free boundary is zero for each t-level.
Analysis of the hydrostatic approximation in oceanography with compression term
Analysis of the hydrostatic approximation in oceanography with compression term
Analysis of the hydrostatic approximation in oceanography with compression term
The hydrostatic approximation of the incompressible 3D stationary Navier-Stokes equations is widely used in oceanography and other applied sciences. It appears through a limit process due to the anisotropy of the domain in use, an ocean, and it is usually studied as such. We consider in this paper an equivalent formulation to this hydrostatic approximation that includes Coriolis force and an additional pressure term that comes from taking into account the pressure in the state equation for...
Analysis of the hydrostatic approximation in oceanography with compression term
The hydrostatic approximation of the incompressible 3D stationary Navier-Stokes equations is widely used in oceanography and other applied sciences. It appears through a limit process due to the anisotropy of the domain in use, an ocean, and it is usually studied as such. We consider in this paper an equivalent formulation to this hydrostatic approximation that includes Coriolis force and an additional pressure term that comes from taking into account the pressure in the state equation for...
Analysis of the mushy region in conduction-convection problems with change of phase.
Analysis of the Schwarz algorithm for mixed finite elements methods