• Corpus ID: 236772305

On the finite element approximation of a semicoercive Stokes variational inequality arising in glaciology

@article{Diego2021OnTF,
  title={On the finite element approximation of a semicoercive Stokes variational inequality arising in glaciology},
  author={G. G. de Diego and Patrick E. Farrell and Ian J. Hewitt},
  journal={ArXiv},
  year={2021},
  volume={abs/2108.00046}
}
. Stokes variational inequalities arise in the formulation of glaciological problems involving contact. We consider the problem of a marine ice sheet with a grounding line, although the analysis presented here is extendable in a straightforward manner to other contact problems in glaciology, such as that of subglacial cavitation. The analysis of this problem and its discretisation is complicated by the nonlinear rheology commonly used for modelling ice, the enforcement of a friction boundary… 

Figures and Tables from this paper

Numerical approximation of viscous contact problems applied to glacial sliding

This work proposes a novel numerical method based on a mixed formulation with Lagrange multipliers of a variational inequality involving the Stokes equation for solving viscous contact problems and uses this numerical scheme to reconstruct friction laws for glacial sliding with cavitation.

References

SHOWING 1-10 OF 56 REFERENCES

Numerical approximation of viscous contact problems applied to glacial sliding

This work proposes a novel numerical method based on a mixed formulation with Lagrange multipliers of a variational inequality involving the Stokes equation for solving viscous contact problems and uses this numerical scheme to reconstruct friction laws for glacial sliding with cavitation.

Analysis and Finite Element Approximation of a Nonlinear Stationary Stokes Problem Arising in Glaciology

Several algorithms (including Newton's method) are proposed to solve the nonlinearity of the Stokes problem and are proved to be convergent and the existence and the uniqueness of a weak solution are proved.

Well-Posedness Results for a Nonlinear Stokes Problem Arising in Glaciology

This work considers the boundary conditions proposed by Schoof and extends his well-posendess results to the Stokes case, and proves an existence result for nonlocal friction in the nonlinear, incompressible Stokes model.

Modélisation, analyse mathématique et simulation numérique de la dynamique des glaciers

We address the free boundary problem that consists in finding the shape of a three dimensional glacier over a given period and under given climatic conditions. Glacier surface moves by sliding,

COULOMB FRICTION AND OTHER SLIDING LAWS IN A HIGHER-ORDER GLACIER FLOW MODEL

We consider a widely used higher-order glacier flow model with a variety of parametrizations of wall slip, including Coulomb friction, regularized Coulomb friction laws and a power law.

A sliding law for glaciers of constant viscosity in the presence of subglacial cavitation

  • A. Fowler
  • Mathematics
    Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1986
A method of solution for the problem of slow flow of a Newtonian viscous glacier slipping over a rough bed is constructed, for the case where cavities form when the lubricating water film pressure

Error estimates for the approximation of semicoercive variational inequalities

Summary. An abstract error estimate for the approximation of semicoercive variational inequalities is obtained provided a certain condition holds for the exact solution. This condition turns out to

Finite‐element modeling of subglacial cavities and related friction law

[1] Sliding velocity and basal drag are strongly influenced by changes in subglacial water pressure or subglacial water storage associated with opening and closing of water cavities in the lee of

General theory of subglacial cavitation and sliding of temperate glaciers

Abstract Earlier theories of Weertman and the present author are reviewed and compared; both are insufficient to account for the facts observed at the tongue of the Allalingletscher. A calculation of

The effect of cavitation on glacier sliding

  • C. Schoof
  • Engineering
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2005
Basal sliding is one of the most important components in the dynamics of fast–flowing glaciers, but remains poorly understood on a theoretical level. In this paper, the problem of glacier sliding
...