In this paper, a nonlinear problem corresponding to a simplified Oldroyd-B model without convective terms is considered. Assuming the domain to be a convex polygon, existence of a solution is proved for small relaxation times. Continuous piecewise linear finite elements together with a Galerkin Least Square (GLS) method are studied for solving this problem. Existence and a priori error estimates are established using a Newton-chord fixed point theorem, a posteriori error estimates are also derived....
In this paper, a
nonlinear problem corresponding to a simplified Oldroyd-B model
without convective terms is considered. Assuming the domain to be a convex
polygon, existence of a solution
is proved for small relaxation times.
Continuous piecewise linear finite elements together with
a Galerkin Least Square (GLS) method are studied for solving this problem.
Existence and error estimates
are established using a Newton-chord fixed point theorem,
error estimates are also derived.
An Elastic Viscous...
The motion of a three-dimensional glacier is considered. Ice is modeled as an incompressible non-Newtonian fluid. At each time step, given the shape of the glacier, a nonlinear elliptic system has to be solved in order to obtain the two components of the horizontal velocity field. Then, the shape of the glacier is updated by solving a transport equation. Finite element techniques are used to compute the velocity field and to solve the transport equation. Numerical results are compared to experiments...
A simplified stochastic Hookean dumbbells model arising from viscoelastic flows is considered, the convective terms being disregarded.
A finite element discretization in space is proposed.
Existence of the numerical solution is proved for small data, so as error estimates,
using an implicit function theorem and regularity results obtained in [Bonito
(2006) 381–398] for the solution of the continuous problem. error estimates are also derived.
Numerical results with small time...
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