Exact a posteriori error analysis of the least squares finite element method

Applied Mathematics and Computation

Volumn 116, Issue 3, 2000, Pages 297-305

  Liu, Jinn Liang ^a  

^a NATIONAL CHIAO TUNG UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY VALUE PROBLEMS; COMPUTATIONAL COMPLEXITY; ERROR ANALYSIS; LEAST SQUARES APPROXIMATIONS; PARTIAL DIFFERENTIAL EQUATIONS;

ADAPTIVE MESH REFINEMENTS; LEAST SQUARES FUNCTIONALS;

FINITE ELEMENT METHOD;

EID: 0034544411     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(99)00153-8     Document Type: Article

References (28)

1. Adjerid S., Flaherty J.E., Wang Y.J. A posteriori error estimation with finite element methods of lines for 1-D parabolic systems. Numer. Math. 65:1993;1-21.
2. Ainsworth M., Oden J.T. A unified approach to a posteriori error estimation using element residual methods. Numer. Math. 65:1993;23-50.
3. Aziz A.K., Kellogg R.B., Stephens A.B. Least squares methods for elliptic systems. Math. Comput. 44:1985;53-70.
4. Aziz A.K., Leventhal S. Finite lement approximation for first order systems. SIAM J. Numer. Anal. 6:1978;1103-1111.
5. Aziz A.K., Liu J.-L. A weighted least squares method for the backward-forward heat equation. SIAM J. Numer. Anal. 28:1991;156-167.
6. Babuška I., Rheinboldt W.C. Error estimates for adaptive finite element computations. SIAM J. Numer. Anal. 15:1978;736-754.
7. Bank R.E., Weiser A. Some a posteriori error estimators for elliptic partial differential equations. Math. Comput. 44:1985;283-301.
8. Bochev P.B., Gunzburger M.D. Analysis of least-squares finite element methods for the Stokes equations. Math. Comput. 63:1994;479-506.
9. Cai Z., Lazarov R., Manteuffel T.A., McCormick S.F. First-order system least squares for second-order partial differential equations: Part I. SIAM J. Numer. Anal. 31:1994;1785-1799.
10. Carstensen C., Stephan E.P. A posteriori error estimates for boundary element method. Math. Comput. 64:1995;483-500.
11. Chang C.L. Finite element approximation for grad-div type systems in the plane. SIAM J. Numer. Anal. 29:1992;452-461.
12. Chang C.L. An error estimate of the least squares finite element method for the Stokes problem in 3-D. Math. Comput. 63:1994;41-50.
13. Chang C.L., Jiang B.-N. An error analysis of least-squares finite element method of velocity-pressure-vorticity formulation for Stokes problem. Comput. Meth. Appl. Mech. Engrg. 84:1990;247-255.
14. Chang C.L., Yang S.-Y., Hsu C.-H. A least-squares finite element method for incompressible flow in stress-velocity-pressure version. Comput. Meth. Appl. Mech. Engrg. 128:1995;1-9.
15. Demkowicz L., Oden J.T., Ainsworth M., Geng P. Solution of elastic scattering problems in linear acoustics using. h - p boundary element method J. Comput. Appl. Math. 36:1991;29-63.
16. Durán R., Rodriguez R. On the asymptotic exactness of Bank-Weiser's estimator. Numer. Math. 62:1992;297-303.
17. Friedrichs K.O. Symmetric positive differential equations. Comm. Pure Appl. Math. 11:1958;333-418.
18. Jiang B.-N., Carey G.F. Adaptive refinement for least-squares finite elements with element-by-element conjugate gradient solution. Int. J. Numer. Meth. Engrg. 24:1987;569-580.
19. Liu J.-L. On weak residual error estimation. SIAM J. Sci. Comput. 14:1996;1249-1268.
20. Liu J.-L., Lin I.-J., Shih M.-Z., Chen R.-C., Hsieh M.-C. Object oriented programming of adaptive finite element and finite volume methods. Appl. Numer. Math. 21:1996;439-467.
21. Liu J.-L., Rheinboldt W.C. A posteriori finite element error estimators for indefinite elliptic boundary value problems. Numer. Func. Anal. Optimiz. 15:1994;335-356.
22. Oden J.T., Demkowicz L., Rachowicz W., Westermann T.A. Toward a universal. h - p adaptive finite element strategy, Part 2. A posteriori error estimation Comput. Meth. Appl. Mech. Engrg. 77:1989;113-180.
23. Sermer P., Mathon R. Least-squares methods for mixed-type equations. SIAM J. Numer. Anal. 18:1981;705-723.
24. Verfürth R. A posteriori error estimates for the Stokes equations. Numer. Math. 55:1989;309-325.
25. W.L. Wendland, Elliptic Systems in the Plane, Pitman, London, 1979.
26. Wendland W.L., Yu D. Adaptive boundary element methods for strongly elliptic integral equations. Numer. Math. 53:1988;539-558.
27. Zhu J.Z., Zienkiewicz O.C. Superconvergence recovery technique and a posteriori error estimators. Int. J. Numer. Meth. Engrg. 30:1990;1321-1339.
28. Zienkiewicz O.C. Computational mechanics today. Int. J. Numer. Meth. Engrg. 34:1992;9-33.