A Robust Weak Galerkin Finite Element Method for Linear Elasticity with Strong Symmetric Stresses
2016 ◽
Vol 16
(3)
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pp. 389-408
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Keyword(s):
A Priori
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AbstractThis paper proposes and analyzes a weak Galerkin (WG) finite element method with strong symmetric stresses for two- and three-dimensional linear elasticity problems on conforming or nonconforming polygon/polyhedral meshes. The WG method uses piecewise-polynomial approximations of degreesk(${\geq 1}$) for the stress,${k+1}$for the displacement, andkfor the displacement trace on the inter-element boundaries. It is shown to be equivalent to a hybridizable discontinuous Galerkin (HDG) finite element scheme. We show that the WG methods are robust in the sense that the derived a priori error estimates are optimal and uniform with respect to the Lamé constant λ. Numerical experiments confirm the theoretical results.
2017 ◽
Vol 74
(6)
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pp. 1379-1398
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Keyword(s):
2021 ◽
Vol 383
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pp. 113124
2020 ◽
Vol 28
(2)
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pp. 75-98
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2020 ◽
Vol 13
(2)
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pp. 281-295
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2018 ◽
Vol 36
(4)
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pp. 469-491
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2018 ◽
Vol 18
(2)
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pp. 223-236
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2009 ◽
Vol 231
(2)
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pp. 526-540
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