Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. Part I: Low order conforming, nonconforming, and mixed FEM

Mathematics of Computation

Volumn 71, Issue 239, 2002, Pages 945-969

  Carstensen, Carsten ^a   Bartels, Sören ^a  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

A posteriori error estimates; Adaptive algorithm; Finite element method; Mixed finite element method; Nonconforming finite element method; Reliability; Residual based error estimate

Indexed keywords

EID: 0036340806     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-02-01402-3     Document Type: Article

References (31)

1. Remarks around 50 lines of Matlab: Short finite element implementation
2. Error estimators for a mixed method
3. Error estimates for adaptive finite element computations
4. Validation of a posteriori error estimators by numerical approach
5. Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. Part II: Higher order FEM
6. A feed-back approach to error Control in finite element methods: Basic analysis and examples
7. A posteriori error estimators for the Raviart-Thomas element
8. The mathematical theory of finite element methods
9. A posteriori error estimate for the mixed finite element method
10. Quasi interpolation and a posteriori error analysis in finite element method
11. Constants in Clément-interpolation error and residual based a posteriori error estimates in Finite Element Methods
12. A posteriori error control in low-order finite element discretisations of incompressible stationary flow problems
13. Averaging technique for FE - A posteriori error control in elasticity. Part I: Conforming FEM
14. Averaging technique for FE - A posteriori error control in elasticity. Part II: λ-independent estimates
15. Averaging technique for FE - A posteriori error control in elasticity. Part III: Locking-free nonconforming FEM
16. Edge residuals dominate a posteriori error estimates for low order finite element methods
17. Approximation by finite element functions using local regularization
18. A posteriori error estimators for nonconforming finite element methods
19. On the asymptotic exactness of error estimators for linear triangular elements
20. Introduction to adaptive methods for differential equations
21. Asymptotically exact a posteriori error estimators for the pointwise gradient error on each element in irregular meshes. Part 1: A smooth problem and globally quasi-uniform meshes
22. Element-oriented and edge-oriented local error estimators for nonconforming finite element methods
23. A posteriori error estimates for nonconforming finite element schemes
24. Some remarks on Zienkiewicz-Zhu estimator
25. A posteriori error analysis in the finite element method. Finite element methods. 50 years of the Courant element
26. A simple error estimator and adaptive procedure for practical engineering analysis