This article discusses the numerical approximation of time dependent Ginzburg-Landau equations. Optimal error estimates which are robust with respect to a large Ginzburg-Landau parameter are established for a semi-discrete in time and a fully discrete approximation scheme. The proofs rely on an asymptotic expansion of the exact solution and a stability result for degree-one Ginzburg-Landau vortices. The error bounds prove that degree-one vortices can be approximated robustly while unstable higher...

A linearly convergent iterative algorithm that approximates the rank-1 convex envelope ${f}^{rc}$ of a given function $f:{\mathbb{R}}^{n\times m}\to \mathbb{R}$, i.e. the largest function below $f$ which is convex along all rank-1 lines, is established. The proposed algorithm is a modified version of an approximation scheme due to Dolzmann and Walkington.

This article discusses the numerical approximation of
time dependent Ginzburg-Landau equations. Optimal
error estimates which are robust with respect
to a large Ginzburg-Landau parameter are established for a
semi-discrete in time and a fully discrete approximation
scheme. The proofs rely on an asymptotic
expansion of the exact solution and a stability result
for degree-one Ginzburg-Landau vortices. The error bounds
prove that degree-one vortices can be approximated robustly
while unstable higher...

A linearly convergent iterative algorithm that approximates the
rank-1 convex envelope ${f}^{rc}$ of a given function $f:{\mathbb{R}}^{n\times m}\to \mathbb{R}$,
the largest function below which is convex along all rank-1 lines, is
established. The proposed algorithm is a modified version of an approximation
scheme due to Dolzmann and Walkington.

We consider a viscoelastic solid in Kelvin-Voigt rheology exhibiting also plasticity with hardening and coupled with heat-transfer through dissipative heat production by viscoplastic effects and through thermal expansion and corresponding adiabatic effects. Numerical discretization of the thermodynamically consistent model is proposed by implicit time discretization, suitable regularization, and finite elements in space. Fine estimates are derived, and convergence is proved by careful successive...

We consider a viscoelastic solid in Kelvin-Voigt rheology exhibiting
also plasticity
with hardening and coupled with heat-transfer
through dissipative heat production by viscoplastic effects
and through thermal expansion and corresponding adiabatic effects.
Numerical discretization of the thermodynamically consistent model
is proposed by implicit time discretization, suitable regularization,
and finite elements in space. Fine estimates are derived,
and convergence is proved by careful successive...

We investigate the evolution of an almost flat membrane
driven by competition of the homogeneous, Frank, and
bending energies as well
as the coupling of the local order of the constituent molecules
of the membrane to its curvature.
We propose an alternative to
the model in [J.B. Fournier and P. Galatoa,
(1997) 1509–1520; N. Uchida,
(2002) 040902] which replaces
a Ginzburg-Landau penalization for the length of the
order parameter by a rigid constraint.
We introduce...

Download Results (CSV)