Professor Benqi Guo


Publications

  1. B. Q. Guo and I. Babuska,  Local Jacobi Operator and Application to the p version of Finite Element Method in Two Dimensions, (2008), ICES Report 08-11, University of Texas at Austin.

  2. B. Q. Guo and I. Babuska,   Mathematical Framework for Lattice Problems, 2006.  Numer. Anal. Modeling (2006),1-35.

  3. B. Q. Guo and J. Zhang,   Stable and Compatible Polynomial Extensions in Three demensions and Applications to the p and h-p Finite Element Method, preprint, 2006.

  4. B. Q. Guo and J. Zhang,   Constructive Proof for Polynomial Extensions in Two demensions and Application to the h-p Finite Element Method, preprint, 2006.

  5. B. Q. Guo,  Approximation Theory for the p-Version FEM in the Framework of Jacobi-weighted Besov and Sobolev Spaces, Part 1: Approximabilities of Singular Functions, Preprint   NI04010-CPD,  Isaac Newton Institute for Mathematical Science, Cambridge University, UK., 2004, and SIAM J. Numer  Anal. 44(2006), 246-269.

  6. B. Q. Guo and Schwab, C.,  Analytical Regularity of Stokes Flow on Polygonal Domains in countably Normed spaces, J. Comp. Appl. Math.  190(2006), 175-201, and Tech. Report of ETHZ, 12-2000, 2000.

  7. B. Q. Guo and N. Heuer, The Optimal Convergence of the h-p Version of the Boundary Element Method with Quasiuniform Meshes for Elliptic Problems on Polygonal Domains, Advances in Computational Mathematics (AICM) 24 (2006),353,374, and Preprint NI03030, Isaac Newton Institute for Mathematical Sciences, Cambridge University, U.K.,2003.

  8. B. Q. Guo and W. Sun,  The Optimal Convergence of the h-p Version of The Finite Element Method with Quasiuniform Meshes, 2006. SIAM J. Numer. Anal.

  9. B. Q. Guo,  Recent Progress in A-posteriori Error Estimation for the p-version of Finite Element Method,  Recent Advances in Adaptive, eds.  Z-C. Shi, Z. Chen, T.Tang and D.Yu, AMS, Comtemporary Mathematics 383 (2005), 47-61.

  10. W. Cao and B. Q. Guo,  Preconditioning for the p-Version Boundary Element Method in Three Dimensions with Triangular Elements, J. of Korean Math. Soc., 41(2004), 345-368. 

  11. B. Q. Guo, Best approximation for the p-Version of FEM in Three Dimensions in the Framework of Jacobi-weighted Besov Spaces,  Current Trends in Scientific Computing edt. Z. Chen, R. Glowinski and K. Li, AMS, Contemporary Mathematics, 329(2003), 139-156.

  12. B. Q. Guo and N. Heuer, The Optimal Convergence of the p-Version of the Boundary Element Method in Two Dimensions,  Numer. Math., 98 (2004), 499-538.

  13. B. Q. Guo, Final Progress Report to U.S. Army Research Office : Mathematical Framework for Problems of Unbounded Lattices.

  14. B. Q. Guo, Unstructured Lattices in Entire Spaces, Preprint, 2002.

  15. B. Q. Guo and W. Cao , A Preconditioner with Inexact Element Face Solvers for the 3- Dimensional P-version Finite Element Methods, J. Comp. Appl. Math. 144(2002),131-144.

  16. I. Babuska and B. Q. Guo, Direct and Inverse Approximation Theorems of the p Version of Finite Element Method in the Framework of Weighted Besov Spaces, Part 1: Approximability of functions in weighted Besov spaces, TICAM Reprot 31, 1999. and SIAM J. Numer. Anal, 39 (2002). 1512-1538.

  17. I. Babuska and B. Q. Guo, Direct and Inverse Approximation Theorems of the p Version of Finite Element Method in the Framework of Weighted Besov Spaces,  Part 2: Optimal convergence of the p-version finite element solutions TICAM Reprot 32, 1999, and M3AS 12(2002), 689-719.

  18. B. Q. Guo and Mark Ainsworth, Iterative Sub-structuring for the h-Version Boundary Element Approximation of the Hypersingular Operator in Three Dimensions,  Applicable Sciences 81(2002), 241-280.

  19. I. Babuska and B. Q. Guo, Optimal Estimates on Lower and Upper Bound of Approximation Error of the p-Version of the Finite Element Method in Two Dimensions, TICAM Report 97-23, 1997, and Numer. Math. 85 (2000), 219-255.

  20. Mark Ainsworth and B. Q. Guo, An Additive Schwarz Method for the p-Version Boundary Element Approximation of the Hypersingular Operator in Three Dimensions, Numer. Math. 85, (2000), 343-366.

  21. W. Cao and B. Q. Guo, Preconditioners on  Element Interfaces for the p Version and Spectral Element Method,  SIAM J. Sci. Comput. 21 (1999). 522-551.

  22. I. Babuska and B. Q. Guo,  Direct and Inverse Approximation Theorems of the p Version of Finite Element Method in the Framework of Weighted Besov Spaces, Part 3: Inverse Approximation Theorems, TICAM Reprot 33,1999.

  23. B. Q. Guo and E. Stephan, The h-p Version of the Coupling of Finite Element and Boundary Element Method in Polyhedral Domains, Numer. Math. 80, (1998), 87-107.

  24. B. Q. Guo and W. Cao, Domain Decomposition Method for the h-p Version Finite Element Method, Comp. Meth. Appl. Mech. Engrg. 157, 425-440, 1998.

  25. B. Q. Guo and W. Cao, Additive Schwarz Method for the h-p Version of the finite Element Method in Two Dimensions, SIAM J. Sci. Comput. 18, 1267-1288, 1997.

  26. B. Q. Guo and W. Cao, An Iterative and Parallel Solver Based on Domain Decompositions for the h-p Version of the Finite Element Method, J.  Compt. & Appl. Math. 83, 71-85, 1997.

  27. B. Q. Guo and I. Babuska, Regularity of the Solution of Elliptic Problems on Nonsmooth Domains in R3 , Part 1:Countably Normed Spaces on Polyhedral Domains, Proceeding of Royal Society of Edinburgh, 127A, 77-126, 1997.

  28. B. Q. Guo and I. Babuska, Regularity of the Solution of Elliptic Problems on Nonsmooth Domains in R3 , Part 2: Regularity in Neighborhoods of Edges, Proceeding of Royal Society of Edinburgh, 127A, 517-545, 1997.

  29. B. Q. Guo and W. Cao, Inexact Solvers on Element Interfaces for the p and h-p Finite Element Method, 1997, Comput. Methods. Appl. Mech. Engrg. 150 (1977), 173-189.

  30. B. Q. Guo and W. Cao, A preconditioner for the h-p Version of the Finite Element Method in Two Dimensions, Numer. Math,. Vol. 75, (1996), 59-77.

  31. B. Q. Guo, E. Stephan and N. Heuer, The h-p Version of Boundary Element Method for Transmission Problems with Piecewise Analytical Data. SIAM J.  Numer.  Anal. 33, 789-808,  1996.

  32. I. Babuska and B. Q. Guo, Approximation Properties of the h-p version of the Finite Element Method, special issue on p- and hp-method, eds. I. Babuska and T.J. Oden, Comp. Meth. Appl. Mech. Engrg. 133 , 319-346, 1996.

  33. I. Babuska, B. Andersson, B. Q. Guo and H.S. Oh, Finite Element Method for Solving Problems with Singular Solutions, J. Compt. Appl. Math. 74, 51-70, 1996.

  34. B. Q. Guo, State of the Art in the h-p Version of the Finite Element Method, invited lecture, Proceeding of Prague Mathematical Conference, 1996, 111-116, 1996.
     

  35. B. Q. Guo, The h-p Version of the Finite Element Method in R3 : Theory and Algorithm, invited lecture, Proceeding of ICOSAHOM'95, 487-500, eds. A.Ilin and R. Scott, Mathematical Journal of Houston, 1995.

  36. B. Q. Guo, Optimal Finite Element Approaches for Elasticity problems on nonsmooth domains in R3, Computaional Mechanics's 95, Vol. 1, 427-432, eds. S.N. Atluri, G. Yawaga and T.A. Cruse, Springer, 1995.

  37. B. Q. Guo and H. Oh, The Method of Auxiliary Mapping for the Finite Element Solutions of Elliptic Partial Differential Equations on Nonsmooth Domains in R3, 1995.

  38. B. Q. Guo and H. Oh, The h-p Version of The Finite Element Method for Problems with Interfaces, Intl. J. Numer. Methods Engrg., Vol. 37, 1741-1762, 1994.

  39. B. Q. Guo, The h-p Version of the Finite Element Method for Solving Boundary Value Problems in Polyhedral Domains, Boundary Value Problems and Integral Equations in Nonsmooth Domains., 101-120, eds. M. Costabel, M. Dauge, C. Nicaise and Marcel Dekker Inc. 1994.

  40. B. Q. Guo and I. Babuska, On Regularity of Elasticity Problems with Piecewise Analytic Data, Advances in Applied Mathematics 14,  307-347, 1993.

  41. I. Babuska and B. Q. Guo, The h, p and h-p Version of The Finite Element Method, Basic theory and Application, Advances in Engineering Software, Vol. 15, 159-174, 1992. Invited by the editor of the special issue on  Error Estimates and Adaptive Meshes of FEM / BEM.

  42. B. Q. Guo, The Performance of the h, p and h-p Version of the Finite Element Method on Crack Problems, Proceeding of The Thirteenth Canadian Annual Applied Mechanics Conference, 386-387, Eds. N. Popplewall A.H. Shah, 1991.

  43. B. Q. Guo, The Geometric Mesh and the h-p Version of the Boundary Element Method, Proceeding of The Sixteenth IMACS World Congress on Industrial and Applied Mathematics, 405-406, eds. R. Vichnevetsky & J.J.H. Miller, 1991.

  44. B. Q. Guo, I. Babuska and E. Stephan, On the Exponential Convergence of the h-p Version of Boundary Element Galerkin Methods on Polygon, Math. Meth. in Appl. Sci., Vol 12, 413-427, 1990.

  45. I. Babuska, B. Q. Guo and J. Osborn, The Regularity and Numerical Solutions of Eigenvalue Problems with Piecewise Analytic Data, SIAM J. Numer. Anal.  25, 1534-1560, 1989.

  46. I. Babuska and B. Q. Guo, Regularity of the Solution of Elliptic problems with Piecewise Analytic Data, Part 2: The Trace Spaces and Application to the Boundary Value Problems with Nonhomogeneous Boundary Conditions, SIAM J. Math. Anal. 20, 763-781, 1989.

  47. I. Babuska, B. Q. Guo and M. Suri, Implementation of Nonhomogeneous Dirichlet Boundary Condition in the p-version of the Finite Element Method, Impact of Computing in Sci. & Engrg. Vol. 1, 36-63, 1989.

  48. I. Babuska and B. Q. Guo, The h-p Version of the Finite Element Method for Problems with Non-homogeneous Essential Boundary Conditions, Comp. Meth. Appl. Mech. Engrg, 74, 1-28, 1989.

  49. I. Babuska and B. Q. Guo, Countably Normed Spaces and the h-p Version of the Finite Element Method, Numerical and Applied Mathematics, 525-530, Ed., C. Brezinski, 1989.

  50. B. Q. Guo, E.  Stephan and T. Petersdorff, An h-p Version of BEM for Plane Mixed Boundary Value Problems, Advances in Boundary Elements 11, 95-102, 989.

  51. I. Babuska and B. Q. Guo, Regularity of the Solution of Elliptic Problems with Piecewise Analytic Data, Part 1: Boundary Value Problems for Linear Elliptic Equations of Second Order, SIAM J. Math. Anal. 19, 172-203, 1988.

  52. I. Babuska and B. Q. Guo, The h-p Version of the Finite Element Method with Curved Boundary, SIAM J. Numer. Anal. 24, 837-861, 1988.

  53. B. Q. Guo, The h-p Version of the Finite Element Method for Elliptic Equation of Order 2m, Numer. Math., Vol. 53, 199-224,  1988.

  54. I. Babuska and B. Q. Guo, The Theory and Practice of the h-p Version of the Finite Element Method, Computer Method in Partial Differential Equations VI, 241-247, Eds. R. Vichnevetsky & R. S. Stepleman, 1987.

  55. B. Q. Guo and I. Babuska, The h-p Version of the Finite Element Method, Part 1: The Basic Approximation Results, Comp. Mech., Vol. 1,  22-41, 1986.

  56. B. Q. Guo and I. Babuska, The h-p Version of the Finite Element Method, Part 2: The General Results and Application, Comp. Mech. , Vol. 1, 203-220, 1986.

  57. B. Q. Guo, The h-p Version of the Finite Element Method with C'-Continuity for Fourth Order Elliptic Problems, Report No. 86-5, Department of Mathematics, Carnegie-Mellon

  58. B. Y. Guo and B. Q. Guo, Numerical Solution of Naiver-Stokes Equation, Acta Mech. Sinica, 1978.

 

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