The Hellan-Herrmann-Johnson method: some new error estimates and postprocessing

Author:
M. I. Comodi

Journal:
Math. Comp. **52** (1989), 17-29

MSC:
Primary 65N30; Secondary 73C35

DOI:
https://doi.org/10.1090/S0025-5718-1989-0946601-7

MathSciNet review:
946601

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Abstract: We analyze the behavior of the mixed Hellan-Herrmann-Johnson method for solving the biharmonic problem . We show a superconvergence result for the distance between (the approximation of the displacement) and (where is a suitable projection operator). If the discrete equations are solved (as is usually done) by using interelement Lagrange multipliers, our superconvergence result allows us to prove the convergence, in suitable norms, of the Lagrange multipliers to the normal derivative of the displacement, and to construct a new approximation of which converges to faster than .

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DOI:
https://doi.org/10.1090/S0025-5718-1989-0946601-7

Article copyright:
© Copyright 1989
American Mathematical Society