594 research outputs found
Finite-element approximation of a nonlinear degenerate parabolic system describing bacterial pattern formation
Accepted versio
Convergence of a finite-element approximation of surfactant spreading on a thin film in the presence of van der Waals forces
A two-stage planning model for power scheduling in a hydro-thermal system under uncertainty
Accepted versio
Stable Numerical Approximation of Two-Phase Flow with a Boussinesq--Scriven Surface Fluid
PARAMETRIC APPROXIMATION OF WILLMORE FLOW AND RELATED GEOMETRIC EVOLUTION EQUATIONS
Accepted versio
A stable numerical method for the dynamics of fluidic membranes
We develop a finite element scheme to approximate the dynamics of two and three dimensional fluidic membranes in Navier–Stokes flow. Local inextensibility of the membrane is ensured by solving a tangential Navier–Stokes equation, taking surface viscosity effects of Boussinesq–Scriven type into account. In our approach the bulk and surface degrees of freedom are discretized independently, which leads to an unfitted finite element approximation of the underlying free boundary problem. Bending elastic forces resulting from an elastic membrane energy are discretized using an approximation introduced by Dziuk (2008). The obtained numerical scheme can be shown to be stable and to have good mesh properties. Finally, the evolution of membrane shapes is studied numerically in different flow situations in two and three space dimensions. The numerical results demonstrate the robustness of the method, and it is observed that the conservation properties are fulfilled to a high precision
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Finite element approximation of a sixth order nonlinear degenerate parabolic equation
We consider a finite element approximation of the sixth order nonlinear degenerate parabolic equation ut = ?.( b(u)?
2u), where generically b(u) := |u|? for any given ? ? (0,?). In addition to showing well-posedness of our approximation, we prove convergence in space dimensions d ? 3. Furthermore an iterative scheme for solving the resulting nonlinear discrete system is analysed. Finally some numerical experiments in one and two space dimensions are presented
Parametric approximation of surface clusters driven by isotropic and anisotropic surface energies
Published versio
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