Adaptive finite elements for obstacle problems

Abstract

We summarise three applications of the obstacle problem to membrane contact, elastoplastic torsion and cavitation modelling, and show how the resulting models can be solved using mixed finite elements. It is challenging to construct fixed computational meshes for any inequality-constrained problem because the coincidence set has an unknown shape. Consequently, we demonstrate how $h$-adaptivity can be used to resolve the unknown coincidence set. We demonstrate some practical challenges that must be overcome in the application of the adaptive method.

A misleading explanation of the "diffusion parameter" was corrected in revision v2

References in corpus (7)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Array Programming with NumPy
• Nonlinear Reynolds equation for hydrodynamic lubrication
• Galerkin least squares finite element method for the obstacle problem
• An adaptive finite element method for the inequality-constrained Reynolds equation
• A stabilised finite element method for the plate obstacle problem
• A posteriori estimates for conforming Kirchhoff plate elements

Cited by in corpus (1)

• A short perspective on a posteriori error control and adaptive discretizations