HP-Adaptivity Papers

  1. Ainsworth, M. and Craig, A.W., A Posteriori error estimators in the finite element method, Numer. Math., pp. 429-463, 60, (1991).
  2. Ainsworth, M., and Oden, J. T., ``A Unified Approach to A Posteriori Error Estimation Using Element Residual Methods,'' TICOM Report 91-03, 1991.
  3. Ainsworth, M. and Oden, J.T., ``A Unified Approach to A Posteriori Error Estimation Based on Element Residual Methods, Numer. Math. (To appear), (1992).
  4. Ainsworth, M., and Oden, J. T., ``A Unified Approach to A Posteriori Error Estimation Using Element Residual Methods,'' TICOM Report 91-03, 1991.
  5. Ainsworth, M. and Oden, J.T., ``An Optimal Order Process for Calculating Self-Equilibrating Fluxes From hp- Finite Element Approximations", (in preparation).
  6. Ainsworth, M. and Oden, J.T., A procedure for a posteriori error estimation for h-p finite element methods, Comp. Meth. Appl. Mech. Eng., (To appear), (1992).
  7. Ainsworth, M. and Oden, J.T., A Posteriori Error Estimators for Second Order Elliptic Systems: Part 1. Theoretical Foundations and A Posteriori Error Analysis, Computers and Mathematics, (To appear), (1992).
  8. Ainsworth, M., Oden, J.T., and Wu, W., A Posteriori Error Estimators for h-p Finite Element Approximations in Linear Elastostatics, (To appear), (1992).
  9. Ainsworth, M., Zhu, J.Z., Craig, A.W., and Zienkiewicz, O.C., ``Analysis of the Zienkiewicz-Zhu Error Estimator," Int. J. Num. Meth. Eng., 28, pp. 2161-2174, 1989.
  10. Babuska, I., and Dorr, M. R., ``Error Estimates for the Combined h- and p- Versions of Finite Element Method,'' Numer. Math., 37, 1981, pp. 252-277.
  11. Babuska, I., and Guo, B., ``The h-p Version of the Finite Element Method for Problems with Nonhomogeneous Essential Boundary Conditions,'' Comp. Meth. Appl. Mech. Eng., Vol 74, pp. 1-28, 1989.
  12. Babuska, I. and Miller, A.D., ``A Feedback Finite Element Method With A Posteriori Estimation: Part 1," Comp. Meth. Appl. Mech. Eng., Vol 61, pp. 1-40, 1987.
  13. Babuska, I. and Miller, A., ``The postprocessing approach in the finite element method. Part I: Calculation of displacements, stresses and other higher derivatives of the displacements, Int. J. Num. Meth. Eng., 20, pp. 1085-1109, (1984).
  14. Babuska, I. and Miller, A., The postprocessing approach in the finite element method. Part II: The calculation of stress intensity factors, Int. J. Num. Meth. Eng., 20, pp. 1111- 1129, (1984).
  15. Babuska, I. and Miller, A., The postprocessing approach in the finite element method. Part III: A posteriori error estimates and adaptive mesh selection, Int. J. Num. Meth. Eng., 20, pp. 2311- 2324, (1984).
  16. Babuska, I., and Rheinboldt, W. C., ``A Posteriori Error Estimates for the Finite Element Method,'' International Journal for Numrical Methods in Engineering, Vol. 12, pp. 1597-1615, 1978.
  17. Babuska, I., and Rheinboldt, W. C., ``Error Estimates for Adaptive Finite Element Computations,'' SIAM Journal of Numerical Analysis, Vol. 15, No. 4, pp. 736-753, 1978.
  18. Babuska, I., and Rheinboldt, W. C., ``Reliable Error Estimation and Mesh Adaptation for the Finite Element Method,'' Computational Methods in Nonlinear Mechanics, Edited by J. T. Oden, North Holland, N.Y., pp. 67-108, 1980.
  19. Babuska, I., Szabo, B. A., and Katz, I. N., ``The hp-Version of the Finite Element Method,'' SIAM J. Numer. Anal., 18, 1981, pp. 515-545.
  20. Babuska, I., and Suri, M., ``The h-p Version of the Finite Element Method With Quasiuniform Meshes,'' Mathematical Modeling and Numerical Analysis, 21 (2), pp. 199-238, 1987.
  21. Babuska, I., and Suri, M., ``The Optimal Convergence Rate of the hp-Version of the Finite Element Method,'' SIAM J. Numer. Anal., Vol. 24, No. 4, pp. 750-776, 1987.
  22. Babuska, I., and Suri, M., ``The Treatment of Nonhomogeneous Direchlet Boundary Conditions by the hp-Version of the Finite Element Method,'' Preprint 1987.
  23. Babuska, I., and Suri, M., ``The hp-Version of the Finite Element Method for Constraint Boundary Conditions,'' Institute for Physical Science and Technology, Technical Note BN-1064, April 1987.
  24. Bank, R. E., ``Analysis of Local A Posteriori Error Estimates for Elliptic Problems,'' in Accuracy Estimates and Adaptive Refinements in Finite Element Computations, Edited by I. Babuska, et al., John Wiley and Sons, Ltd., Chichester, pp. 119-128, 1986.
  25. Bank, R. E., Sherman, A., H., and Weiser, A., ``Refinement Algorithms and Data Structures for Regular Mesh Refinement," in Scientific Computing, R. Stepleman, et al. (Eds), IMACS, North Holland, 1983.
  26. Bank, R. E., and Weiser, A., ``Some A Posteriori Error Estimates for Elliptic Partial Differential Equations,'' Mathematics of Computation, Vol. 44, No. 170, pp. 283-301, 1985.
  27. Bank, R. E., and Welfert, B. D., ``A Posteriori Error Estimates for Stokes' Equations,'' SIAM J. N. A., 1991.
  28. Bass, J. M., and Oden, J. T., ``Adaptive Finite Element Methods for a Class of Evolution Problems in Viscoplasticity,'' International Journal of Engineering Science, Vol. 25, No. 6, pp. 623-653, 1987.
  29. J.U. Brackbill, J.S. Saltzman,``Adaptive Zoning for Singular Problems in Two Dimensions.", Journal of Computational Physics, Vol. 46, pp. 342-368, 1982.
  30. R. Carcaillet, G. Dulikravich, and S.R. Kennon, ``Generation of Solution-Adaptive Computational Grids Using Optimization.", Comput. Methods Appl. Mech. Engng., 57, pp. 279-295, (1986).
  31. Demkowicz, L., Devloo, Ph., and Oden, J. T., ``On an hp-Type Mesh Refinement Strategy Based on a Minimization of Interpolation Error,'' Computer Methods in Applied Mechanics and Engineering, Vol. 53, No. 3, pp. 67-89, 1985.
  32. Demkowicz, L., and Oden, J. T., ``On a Mesh Optimization Based on a Minimization of Interpolation Error,'' International Journal of Engineering Science, Vol. 24, No. 1, pp. 55-68, 1986.
  33. Demkowicz, L., and Oden, J. T., ``A Review of Local Mesh Refinement Techniques and Corresponding Data Structures in hp-type Adaptive Finite Element Methods," TICOM Report 88-02, The Texas Institute for Computational Mechanics, The University of Texas at Austin, Texas, 78712.
  34. Demkowicz, L., Oden, J. T., and Rachowicz, W., ``A New Finite Element Method for Solving Compressible Navier-Stokes Equations Based on an Operator Splitting Method and h-p Adaptivity,'' Comp. Meth. in Appl. Mech. and Engrg. Vol. 84, 1990, pp. 275-326.
  35. Demkowicz, L., Oden, J. T., Rachowicz, W., and Hardy, O., ``Toward a Universal h-p Adaptive Finite Element Strategy. Part 1: Constrained Approximation and Data Structure,'' Comp. Meth. in Appl. Mech. and Engrg., 77, pp. 79-112, 1989.
  36. Demkowicz, L., Oden, J. T., Rachowicz, W., and Hardy, O., ``An h-p Taylor-Galerkin Finite Element Method for Compressible Euler Equations'' Comp. Meth. in Appl. Mech. and Engrg. Vol. 88, 3 1991, pp. 363-396.
  37. Demkowicz, L., Oden, J.T., and Strouboulis, T., ``Adaptive Finite Element Methods for Flow Problems with Moving Boundaries. Part I. Variational Principles and A Posteriori Estimates," Computer Methods in Applied Mechanics and Engineering, Vol. 46, pp. 217-251, 1984.
  38. Devloo, Ph., Oden, J. T., and Pattani P., ``An h-p Adaptive Finite Element Method for the Numerical Simulation of Compressible Flow,'' Comp. Meth. in Appl. Mech. and Engrg., Vol. 70, pp. 203-235, 1988.
  39. Devloo, Ph., Oden, J. T., and Strouboulis, T., ``Implementation of an Adaptive Refinement Technique for the SUPG Algorithm,'' Computer Methods in Applied Mechanics and Engineering, Vol. 61, pp. 339-358, 1987.
  40. Demkowicz, L., and Swierczek, M., ``An Adaptive Finite Element Method for a Class of Variational Inequalities,'' Proceedings of Italian-Polish Symposium on Continuum Mechanics, Bologna 1987.
  41. Gui, W., and Babuska, I., ``The h, p, and h-p Versions of the Finite Element Method in One Dimension, Parts 1, 2, 3,'' Numer. Math., 49 (1986), 577-683.
  42. Guo, B., and Babuska, I., ``The h-p Version of the Finite Element Method,'' Parts 1 and 2, Computational Mechanics (1986) 1, 21-41, 203-220.
  43. Jacquette, O., ``A Mechanical Model for a New Grid Generation Method in Computational Fluid Dynamics.", Comput. Methods Appl. Mech. Engng., 66, pp. 323-338, (1988).
  44. Jacquette, O., and J. Cabello, ``A New Variational Method for the Generation of Two- and Three-Dimensional Adapted Grids in Computational Fluid Dynamics.", 7th International Conference for Finite Element Methods in Flow Problems, Huntsville, Alabama, April 3-7, 1989.
  45. Kelly, D. W., ``The Self-Equilibration of Residuals and Complimentary Error Estimates in the Finite Element Method," Int. J. Num Meth. Eng., Vol. 20, pp. 1491-1506, 1984.
  46. S. Kennon and D. Anderson, ``Unstructured Grid Adaption for Non-Convex Domains," in Numerical Grid Generation in Computational Fluid Mechanics (Edited by S. Sengupta, J. Hauser, P.R. Eiseman, and J.F. Thompson), pp. 599-609. Pineridge Press. (1988).
  47. Noor, A.K. and Babuska, I., Quality assessment and control of finite element solutions, Finite Elements and Design, 3, pp. 1-26, (1987).
  48. Oden, J. T., ``Theory and Implementation of High-order Adaptive hp-methods for the Analysis of Incompressible Viscous Flows'' To be published in Computational Nonlinear Mechanics in Aerospace Engineering, a volume in the ``AIAA Progress in Aeronautics and Astronautics'' series, S. N, Atluri, editor.
  49. Oden, J. T., and Demkowicz, L., `` Advances in Adaptive Improvements: A Survey of Adaptive Finite Element Methods in Computational Mechanics,'' State-of-the-Art Surveys in Computational Mechanics, Edited by A. K. Noor and J. T. Oden, A.S.M.E. Publications, N.Y., 1988.
  50. Oden, J. T., Demkowicz, L., Liszka, T. J., Rachowicz, W., ``h-p Adaptive Finite Element Methods for Compressible and Incompressible Flows'' Computing Systems in Eng. Vol.1, Nos 2-4, pp 523-534, 1990.
  51. Oden, J. T., Demkowicz, L., Rachowicz, W., and Westermann, T. A., ``A Posteriori Error Analysis in Finite Elements: The Element Residual Method for Symmetrizable Problems with Applications to Compressible Euler and Navier-Stokes Equations,'' Comp. Meth. in Appl. Mech. and Engrg.: Special Issue: Reliability in Computational Mechanics, Edited by J. T. Oden, Vol. 82, Nos. 1-3, pp. 183-204, 1990.
  52. Oden, J. T., Demkowicz, L., Rachowicz, W., and Westermann, T. A., ``Toward a Universal h-p Adaptive Finite Element Strategy. Part 2: A Posteriori Error Estimation,'' Comp. Meth. in Appl. Mech. and Engrg., 77, pp. 113-180, 1989.
  53. Oden, J.T., Demkowicz, L., Strouboulis, T., and Devloo, P., ``Adaptive Methods for Problems in Solid and Fluid Mechanics," Accuracy Estimates and Adaptive Refinements in Finite Element Computations, Edited by I. Babuska, O.C. Zienkiewicz, J. Gago, and E.R. de A. Oliveira, John Wiley and Sons, Ltd., Chichester, pp. 249-280, 1986.
  54. Oden, J. T., Liszka, T. J., Wu, W., ``An h-p Adaptive Finite Element Method for Incompressible Viscous Flows'', In ``The Mathematics of Finite Elements with Applications'' ed. Whiteman, J. R., Acad. Press., London 1991.
  55. Oden, J. T., Strouboulis, T., and Devloo, Ph., ``Adaptive Finite Element Methods for the Analysis of Inviscid Compressible Flow: I. Fast Refinement/Unrefinement and Moving Mesh Methods for Unstructured Meshes,'' Computer Methods in Applied Mechanics and Engineering, Vol. 59, No. 3, pp. 327-362, 1986.
  56. Rachowicz, W., ``An Evaluation and Comparison of Postprocessing Methods for Finite Element Solution of Elliptic Boundary Value Problems," TICOM Report 87-11, 1987.
  57. Rheinboldt, W. C., and Mesztenyi, Ch. K., ``On a Data Structure for Adaptive Finite Element Mesh Refinement," ACM Transaction on Mathematical Software, Vol. 6, No. 2, pp. 166-187, 1980.
  58. Thareja, R. R., Prabhu, R. K., Morgan, K., Peraire, J., and Soltani, S., ``Applications of an Adaptive Unstructured Solution Algorithm to the Analysis of High Speed Flows,'' AIAA 90-0395, 1990.
  59. Tworzydlo, W. W., and Oden, J. T., ``Toward an Automated Environment in Computational Mechanics,'' prepared for publication in Comp. Meths. Appl. Mech. Engrg.
  60. Tworzydlo, W. W., Oden, J. T., and Thornton, E. A., ``Adaptive Implicit/Explicit Finite Element Methods for Compressible Viscous Flows,'' Comp. Meth. in Appl. Mech. and Engrg., Vol. 95, pp. 397-440, 1992.
  61. Suri, M., ``The hp-Version of the Finite Element Method for Elliptic Problems,'' in Advances in Computer Methods for Partial Differential Equations VI, R. Vichnevetsky and R. S. Stepleman, eds., Publ. IMACS - 1987.
  62. Strang, G. and Fix, G.J., ``An Analysis of the Finite Element Method", Prentice-Hall, 1972.
  63. Verfürth, R., ``A Posteriori Error Estimators for Stokes' Equations,'' Numer. Math., 55, 1989.
  64. Wu, W., and Oden, J. T., " Stability of Mixed and Penalty Approximatins for High Order Finite Element Approximation of the Stokes Problem in Two Dimensions", TICOM report, TR-3-91, Austin 1991.
  65. Zienkiewicz, O.C and Zhu, J.Z., ``A simple error estimator and adaptive procedure for practical engineering analysis, Int. J. Num. Meth. Eng., 24, pp. 337-357, (1987).

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