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Unifying a posteriori error analysis of five piecewise quadratic discretisations for the biharmonic equation.
- Source :
-
Journal of Numerical Mathematics . Mar2024, Vol. 32 Issue 1, p77-109. 33p. - Publication Year :
- 2024
-
Abstract
- An abstract property (H) is the key to a complete a priori error analysis in the (discrete) energy norm for several nonstandard finite element methods in the recent work [Lowest-order equivalent nonstandard finite element methods for biharmonic plates, Carstensen and Nataraj, M2AN, 2022]. This paper investigates the impact of (H) to the a posteriori error analysis and establishes known and novel explicit residual-based a posteriori error estimates. The abstract framework applies to Morley, two versions of discontinuous Galerkin, C0 interior penalty, as well as weakly over-penalized symmetric interior penalty schemes for the biharmonic equation with a general source term in H−2 (Ω). [ABSTRACT FROM AUTHOR]
- Subjects :
- *A posteriori error analysis
*BIHARMONIC equations
*FINITE element method
Subjects
Details
- Language :
- English
- ISSN :
- 15702820
- Volume :
- 32
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Numerical Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 175943508
- Full Text :
- https://doi.org/10.1515/jnma-2022-0092