Categorical representations of categorical groups.
Finite element approximation of finitely extensible nonlinear elastic dumbbell models for dilute polymers
We construct a Galerkin finite element method for the numerical approximation of weak solutions to a general class of coupled FENE-type finitely extensible nonlinear elastic dumbbell models that arise from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The class of models involves the unsteady incompressible Navier–Stokes equations in a bounded domain ⊂ ℝ, = 2 or 3, for the velocity...
An optimal error bound for a finite element approximation of a model for phase separation of a multi-component alloy with non-smooth free energy
Quasi-norm error bounds for the finite element approximation of some degenerate quasilinear elliptic equations and variational inequalities
A priori and a posteriori error bounds for a nonconforming linear finite element approximation of a non-newtonian flow
Finite element approximation of a free boundary problem arising in the theory of liquid drops ans plasma physics
Finite element approximation of kinetic dilute polymer models with microscopic cut-off
We construct a Galerkin finite element method for the numerical approximation of weak solutions to a coupled microscopic-macroscopic bead-spring model that arises from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The model consists of the unsteady incompressible Navier–Stokes equations in a bounded domain Ω ⊂ ,= 2 or 3, for the velocity and the pressure of the fluid, with an elastic extra-stress tensor as right-hand side in the momentum equation....
Finite element approximation of a Stefan problem with degenerate Joule heating
We consider a fully practical finite element approximation of the following degenerate system subject to an initial condition on the temperature, , and boundary conditions on both and the electric potential, . In the above is the enthalpy incorporating the latent heat of melting, is the temperature dependent heat conductivity, and is the electrical conductivity. The latter is zero in the frozen zone, , which gives rise to the degeneracy in this Stefan system....
A quasi-variational inequality problem arising in the modeling of growing sandpiles
Existence of a solution to the quasi-variational inequality problem arising in a model for sand surface evolution has been an open problem for a long time. Another long-standing open problem concerns determining the dual variable, the flux of sand pouring down the evolving sand surface, which is also of practical interest in a variety of applications of this model. Previously, these problems were solved for the special case in which the inequality is simply variational. Here, we introduce a regularized...
Total Flux Estimates for a Finite Element Approximation of the Dirichlet Problem Using the Boundary Penalty Method.
Finite element approximation of a model reaction - diffusion problem with a non-Lipschitz nonlinearity.
Finite Element Approximation of the Dirichlet Problem Using the Boundary Penalty Method.
Finite element approximation of the volume-matching problem.
A Practical Finite Element Approximation of a Semi-Definite Neumann Problem on a Curved Domain.
An optimal error bound for a finite element approximation of a model for phase separation of a multi-component alloy with non-smooth free energy
Using the approach in [5] for analysing time discretization error and assuming more regularity on the initial data, we improve on the error bound derived in [2] for a fully practical piecewise linear finite element approximation with a backward Euler time discretization of a model for phase separation of a multi-component alloy with non-smooth free energy.
Finite element approximation of finitely extensible nonlinear elastic dumbbell models for dilute polymers
We construct a Galerkin finite element method for the numerical approximation of weak solutions to a general class of coupled FENE-type finitely extensible nonlinear elastic dumbbell models that arise from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The class of models involves the unsteady incompressible Navier–Stokes equations in a bounded domain ⊂ ℝ, = 2 or 3, for the velocity...
Finite element approximation of kinetic dilute polymer models with microscopic cut-off
We construct a Galerkin finite element method for the numerical approximation of weak solutions to a coupled microscopic-macroscopic bead-spring model that arises from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The model consists of the unsteady incompressible Navier–Stokes equations in a bounded domain Ω ⊂ , = 2 or 3, for the velocity and the pressure of the fluid, with an elastic extra-stress tensor as right-hand side in the momentum equation....
Finite element approximation of a Stefan problem with degenerate Joule heating
We consider a fully practical finite element approximation of the following degenerate system subject to an initial condition on the temperature, , and boundary conditions on both and the electric potential, . In the above is the enthalpy incorporating the latent heat of melting, is the temperature dependent heat conductivity, and is the electrical conductivity. The latter is zero in the frozen zone, ≤ 0, which gives rise to the degeneracy in this Stefan system. In addition to showing...
Finite element approximation of a two-layered liquid film in the presence of insoluble surfactants
We consider a system of degenerate parabolic equations modelling a thin film, consisting of two layers of immiscible Newtonian liquids, on a solid horizontal substrate. In addition, the model includes the presence of insoluble surfactants on both the free liquid-liquid and liquid-air interfaces, and the presence of both attractive and repulsive van der Waals forces in terms of the heights of the two layers. We show that this system formally satisfies a Lyapunov structure, and a second energy...
A Mixed Formulation of the Monge-Kantorovich Equations
We introduce and analyse a mixed formulation of the Monge-Kantorovich equations, which express optimality conditions for the mass transportation problem with cost proportional to distance. Furthermore, we introduce and analyse the finite element approximation of this formulation using the lowest order Raviart-Thomas element. Finally, we present some numerical experiments, where both the optimal transport density and the associated Kantorovich potential are computed for a coupling problem and problems...
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