Browsing by Author "Grieshaber, B J"

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    Locking-free discontinuous Galerkin methods for problems in elasticity, using linear and multilinear approximations
    (2013) Grieshaber, B J; Reddy, Daya
    With interior penalty discontinuous Galerkin methods well established as locking-free for lowo-rder triangular elements, and thus an effective alternative to the Standard Galerkin method for nearly incompressible materials, substantial numerical evidence in this work shows that this is not the case for quadrilateral elements. Direct comparisons to triangles illustrate the material dependence of three common interior penalty methods for bilinear quadrilaterals, with locking and other manifestations of poor approximations in the near-incompressible regime. To understand this discrepancy with a view to providing a remedy for the problem, an existing convergence analysis for triangles is looked at for possible extension to the case of quadrilaterals. This highlights the need for a suitable interpolant for the error-splitting approach of the proof. To rectify the problem manifesting in the numerical results, a modification to the formulation or elements themselves is necessary, and a preliminary analysis with bilinear elements, assuming the existence of a suitable interpolant with some basic properties, indicates two modifications as potential remedies: edge-term under-integration, and the use of linear rather than multilinear elements.