An a posteriori error estimator for the p- and hp-versions of the finite element method

International Journal for Numerical Methods in Engineering

Volumn 62, Issue 1, 2005, Pages 1-18

  Tarancon J E ^a   Fuenmayor, F J ^a   Baeza, L ^a  

^a UNIVERSITAT POLITÈCNICA DE VALÈNCIA   (Spain)

Author keywords

Error estimation; Finite elements; Hp version; P version

Indexed keywords

ELASTICITY; FINITE ELEMENT METHOD; POLYNOMIALS; PROBLEM SOLVING; RELIABILITY;

ERROR INDICATORS; LINEAR ELASTOSTATIC PROBLEMS; POSTERIORI ERROR ESTIMATORS;

ERROR ANALYSIS;

ERROR; FINITE ELEMENT METHOD;

EID: 11144335943     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.1162     Document Type: Article

References (17)

1. Szabó BA, Actis RL. Finite element analysis in professional practice. Computer Methods in Applied Mechanics and Engineering 1996; 133:209-228.
2. Babuška I, Strouboulis T, Upadhyay CS, Gangaraj SK. A model study of element residual estimators for linear elliptic problems: the quality of the estimators in the interior of meshes of triangles and quadrilaterals. Computers and Structures 1995; 57 6):1009-1028.
3. Ainsworth M, Oden JT. A procedure for a posteriori error estimation for h-p finite element methods. Computer Methods in Applied Mechanics and Engineering 1992; 101:73-96.
4. Ainsworth M, Oden JT. A unified approach to a posteriori error estimation using element residual methods. Numerische Mathematik 1993; 65:23-50.
5. Craig AW, Ainsworth M, Zhu JZ, Zienkiewicz OC. h and h-p version error estimation and adaptive procedures from theory to practice. Engineering with Computers 1989; 5:221-234.
6. Zienkiewiez OC, Zhu JZ, Gong G. Effective and practical h-p version adaptive analysis procedures for the finite element method. International Journal for Numerical Methods in Engineering 1989; 28:879-891.
7. Cugnon F, Beckers P. Error estimation for h- and p-method. Technical Report SA-197, LTAS-Infographie, University of Liège, 1998.
8. Georges MK, Shephard MS. Automated adaptive two-dimensional system for the hp- version of the finite element method. International Journal for Numerical Methods in Engineering 1991; 32:867-893.
9. Bertóti E, Szabó B. Adaptative selection of polynomial degrees on a finite element mesh. International Journal for Numerical Methods in Engineering 1998; 42:561-587.
10. Oh H-S, Batra RC. Application of Zienkiewicz-Zhu's error estimate with superconvergent patch recovery to hierarchical p-refinement. Finite Elements in Analysis and Design 1999; 31:273-280.
11. Szabó BA, Babuška I. Finite Element Analysis. Wiley: New York, 1991.
12. Zienkiewicz OC, Zhu JZ. A simple error estimator and adaptive procedure for practical engineering analysis. International Journal for Numerical Methods in Engineering 1987; 24:337-357.
13. Zienkiewicz OC, Zhu JZ. The superconvergent patch recovery and a posteriori error estimates. Part 1: the recovery technique. International Journal for Numerical Methods in Engineering 1992; 33:1331-1364.
14. Zienkiewicz OC, Zhu JZ. The superconvergent patch recovery and a posteriori error estimates. Part 2: error estimates and adaptivity. International Journal for Numerical Methods in Engineering 1992; 33:1365-1382.
15. Tarancón JE. Estimación y control del error de discretización en el método hp de elementos finitos. Ph.D. Thesis, Departamento de Ingeniería Mecánica y de Materiales, Universidad Politécnica de Valencia, 2002.
16. Babuška I, Strouboulis T, Upadhyay CS. A model study of the quality of a posteriori error estimators for finite element solutions of linear elliptic problems, with particular reference to the behavior near the boundary. International Journal for Numerical Methods in Engineering 1997; 40:2521-2577.
17. Babuška I, Guo BQ. Approximation properties of the h-p version of the finite element method. Computer Methods in Applied Mechanics and Engineering 1996; 133:319-346.