Quasi-optimal adaptive hybridized mixed finite element methods for linear elasticity
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For the planar Navier--Lam\'e equation in mixed form with symmetric stress tensors, we prove the uniform quasi-optimal convergence of an adaptive method based on the hybridized mixed finite element proposed in [Gong, Wu, and Xu: Numer.~Math., 141 (2019), pp.~569--604]. The main ingredients in the analysis consist of a discrete a posteriori upper bound and a quasi-orthogonality result for the stress field under the mixed boundary condition. Compared with existing adaptive methods, the proposed adaptive algorithm could be directly applied to the traction boundary condition and be easily implemented.
2014 ◽
Vol 25
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pp. 530-543
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2018 ◽
Vol 41
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pp. 5493-5505
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2018 ◽
Vol 20
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pp. 333-345
2004 ◽
Vol 19
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pp. 223-228
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2018 ◽
Vol 88
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pp. 14-25
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1993 ◽
Vol 115
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pp. 262-267
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