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Locking-Free DGFEM for Elasticity Problems in Polygons

by Th. P. Wihler

(Report number 2002-14)

Abstract
The h-version of the discontinuous Galerkin finite element method (h-DGFEM) for nearly incompressible linear elasticity problems in polygons is analyzed. It is proved that the scheme is robust (locking-free) with respect to volume locking, even in the absence of H2-regularity of the solution. Furthermore, it is shown that an appropriate choice of the finite element meshes leads to robust and optimal algebraic convergence rates of the DGFEM even if the exact solutions are singular.

Keywords: DGFEM, locking, elasticity problems, singular solutions, graded meshes, discontinuous Galerkin methods

@Techreport{W02_300,
  author = {Th. P. Wihler},
  title = {Locking-Free DGFEM for Elasticity Problems in Polygons},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2002-14},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2002/2002-14.pdf },
  year = {2002}
}

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