Abstract
We study a family of discontinuous Galerkin methods for the displacement obstacle problem of Kirchhoff plates on two and three dimensional convex polyhedral domains, which are characterized as fourth order elliptic variational inequalities of the first kind. We prove that the error in an H 2 -like energy norm is O(h α ) for the quadratic method, where α∈([Formula presented],1] is determined by the geometry of the domain. Under additional assumptions on the contact set such that the solution has improved regularity, we derive the optimal error estimate with α∈(1,[Formula presented]) for the cubic method. Numerical experiments demonstrate the performance of the methods and confirm the theoretical results.
Original language | English |
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Pages (from-to) | 531-547 |
Number of pages | 17 |
Journal | Computer Methods in Applied Mechanics and Engineering |
Volume | 351 |
DOIs | |
Publication status | Published - 1 Jul 2019 |
Keywords
- Discontinuous Galerkin methods
- Displacement obstacle
- Error estimate
- Fourth order variational inequality
ASJC Scopus subject areas
- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- General Physics and Astronomy
- Computer Science Applications