Bibliography for Galerkin's Method

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  1. Generalization of Runge-Kutta discontinuous Galerkin method to LWR traffic flow model with inhomogeneous road conditions.  
    Zhang, Peng; Liu, Ru-Xun
    Numer. Methods Partial Differential Equations  21  (2005),  no. 1, 80--88, MathSciNet.
  2. A Crank-Nicolson and ADI Galerkin method with quadrature for hyperbolic problems.
    Ganesh, M.; Mustapha, K.
    Numer. Methods Partial Differential Equations 21 (2005), no. 1, 57--79, MathSciNet.
  3. 3-Dimensional Implementation Of The Field Iterative Method For Cavity Modeling  PDF  
    C.-F. Wang, Y. Xu, And Y.-B. Gan, Progress In Electromagnetics Research, PIER 47, 27--47, 2004.  
  4. A multipole Galerkin boundary element method for acoustics
    Fischer, Matthias; Gauger, Ute; Gaul, Lothar
    Engineering Analysis with Boundary Elements, v 28, n 2, February, 2004, p 155-162, Compendex.
  5. Iterated discrete polynomially based Galerkin methods
    Kulkarni, Rekha P.; Gnaneshwar, N.
    Applied Mathematics and Computation (New York), v 146, n 1, Dec 30, 2003, p 153-165, Compendex.  
  6. Coupled, forced response of an axially moving strip with internal resonance  PDF  
    C.H. Riedel;  C.A. Tan, International Journal of Non-Linear Mechanics 37 (2002) 101}116.
  7. Richardson extrapolation of iterated discrete Galerkin solution for two-dimensional Fredholm integral equations
    Han G.; Wang R.
    Journal of Computational and Applied Mathematics, 1 February 2002, vol. 139, no. 1, pp. 49-63(15), Ingenta.  
  8. A new mathematical development for radiosity animation with Galerkin
    Didier, Arques; Venceslas, Biri; Sylvain, Michelin
    Computer Animation, Conference Proceedings, 2001, p 201-207, Compendex.
  9. Runge-Kutta discontinuous Galerkin methods for convection-dominated problems
    Cockburn, Bernardo; Shu, Chi-Wang
    Journal of Scientific Computing, v 16, n 3, September, 2001, p 173-261, Compendex.
  10. Wind-driven currents in a sea with a variable eddy viscosity calculated via a Sinc-Galerkin technique
    Winter, D.F.; Bowers, Kenneth L.; Lund, John
    International Journal for Numerical Methods in Fluids, v 33, n 7, Aug, 2000, p 1041-1073, Compendex.
  11. Meshless Galerkin Methods Using Radial Basis Functions  
    Holger Wendland  
    Mathematics of Computation > Vol. 68, No. 228 (Oct., 1999), pp. 1521-1531, Jstor.   
  12. Postprocessing the Galerkin Method: The Finite-Element Case  
    Bosco Garcia-Archilla; Edriss S. Titi  
    SIAM Journal on Numerical Analysis > Vol. 37, No. 2 (Dec., 1999), pp. 470-499, Jstor.   
  13. A Taylor discontinuous Galerkin method for the thermal solution in 3D mold filing.
    Pichelin, E.; Coupez, T.
    Computer methods in applied mechanics and engineering, 1999, vol. 178, no. 1/2, pp. 153, Ingenta.  
  14. An H^1-Galerkin Mixed Finite Element Method for Parabolic Partial Differential Equations  
    Amiya K. Pani  
    SIAM Journal on Numerical Analysis > Vol. 35, No. 2 (Apr., 1998), pp. 712-727, Jstor.   
  15. The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems  
    Bernardo Cockburn; Chi-Wang Shu  
    SIAM Journal on Numerical Analysis > Vol. 35, No. 6 (Dec., 1998), pp. 2440-2463, Jstor.     
  16. Numerical Solution of Parabolic Integro-Differential Equations by the Discontinuous Galerkin Method  
    Stig Larsson; Vidar Thomee; Lars B. Wahlbin  
    Mathematics of Computation > Vol. 67, No. 221 (Jan., 1998), pp. 45-71, Jstor.     
  17. A Taylor-Galerkin Method for Simulating Nonlinear Dispersive Water Waves.
    Ambrosi, D.; Quartapelle, L.
    Journal of computational physics, 1998, vol. 146, no. 2, pp. 546, Ingenta.  
  18. On the Superconvergence of Galerkin Methods for Hyperbolic IBVP  
    David Gottlieb; Bertil Gustafsson; Pelle Olsson; Bo Strand  
    SIAM Journal on Numerical Analysis > Vol. 33, No. 5 (Oct., 1996), pp. 1778-1796, Jstor.      
  19. Extra Smoothness Requirements for Galerkin Methods for the Wave Equation  
    Mark C. Haase  
    SIAM Journal on Numerical Analysis > Vol. 33, No. 5 (Oct., 1996), pp. 1962-1968, Jstor.        
  20. The superconvergence of a Galerkin collocation method for first kind boundary integral equations on smooth curves.    
    Shu, H. Z.    
    J. Comput. Appl. Math. 72 (1996), no. 1, 1--20, MathSciNet.  
  21. A Galerkin-Characteristic Algorithm for Transport-Diffusion Equations  
    Rodolfo Bermejo  
    SIAM Journal on Numerical Analysis > Vol. 32, No. 2 (Apr., 1995), pp. 425-454, Jstor.     
  22. Nonlinear Galerkin Method Using Chebyshev and Legendre Polynomials I. The One-Dimensional Case  
    Jie Shen; Roger Temam  
    SIAM Journal on Numerical Analysis > Vol. 32, No. 1 (Feb., 1995), pp. 215-234, Jstor.      
  23. A Taylor-Galerkin Finite Element Method for the Hydrodynamic Semiconductor Equations.
    Bova, S.; Carey, G. F.
    Ieee transactions on computer-aided design of in, 1995, vol. 14, no. 12, pp. 1437, Ingenta.   
  24. A new direct higher-order Taylor-Galerkin finite element method.
    Youn, Sung-Kie; Park, Sang-Hoon
    Computers & structures, 1995, vol. 56, no. 4, pp. 651, Ingenta.   
  25. Characteristic-Galerkin Methods for Contaminant Transport with Nonequilibrium Adsorption Kinetics  
    C. N. Dawson; C. J. Van Duijn; M. F. Wheeler  
    SIAM Journal on Numerical Analysis > Vol. 31, No. 4 (Aug., 1994), pp. 982-999, Jstor.    
  26. On a Cell Entropy Inequality for Discontinuous Galerkin Methods  
    Guangshan Jiang; Chi-Wang Shu  
    Mathematics of Computation > Vol. 62, No. 206 (Apr., 1994), pp. 531-538, Jstor.     
  27. Global error control for the continuous Galerkin finite element method for ordinary differential equations.    
    Estep, Donald; French, Donald    
    RAIRO Modél. Math. Anal. Numér. 28 (1994), no. 7, 815--852, MathSciNet.  
  28. On the Question of Turbulence Modeling by Approximate Inertial Manifolds and the Nonlinear Galerkin Method  
    John G. Heywood; Rolf Rannacher  
    SIAM Journal on Numerical Analysis > Vol. 30, No. 6 (Dec., 1993), pp. 1603-1621, Jstor.    
  29. A Least Squares Petrov-Galerkin Finite Element Method for the Stationary Navier-Stokes Equations  
    Tian-Xiao Zhou; Min-Fu Feng  
    Mathematics of Computation > Vol. 60, No. 202 (Apr., 1993), pp. 531-543, Jstor.      
  30. A Modification of Taylor-Galerkin Finite Element Method and Its Application.
    Gang, Zhu; Chuan-gang, Gu; Qing-kang, Hu
    Applied mathematics and mechanics, 1993, vol. 14, no. 12, pp. 1173, Ingenta.   
  31. Explicit/Implicit Conservative Galerkin Domain Decomposition Procedures for Parabolic Problems  
    Clint N. Dawson; Todd F. Dupont  
    Mathematics of Computation > Vol. 58, No. 197 (Jan., 1992), pp. 21-34, Jstor.    
  32. A Class of Numerical Algorithms for Large Time Integration: The Nonlinear Galerkin Methods  
    Christophe Devulder; Martine Marion  
    SIAM Journal on Numerical Analysis > Vol. 29, No. 2 (Apr., 1992), pp. 462-483, Jstor.     
  33. Galerkin's method for ordinary differential equations subject to generalized nonlinear boundary conditions.
    Rodríguez, Jesús
    J. Differential Equations 97 (1992), no. 1, 112--126, MathSciNet.  
  34. A Galerkin Method for the Forward-Backward Heat Equation  
    A. K. Aziz; J.-L. Liu  
    Mathematics of Computation > Vol. 56, No. 193 (Jan., 1991), pp. 35-44, Jstor.   
  35. An Alternating Direction Galerkin Method for a Class of Second-Order Hyperbolic Equations in Two Space Variables   
    Ryan I. Fernandes; Graeme Fairweather  
    SIAM Journal on Numerical Analysis > Vol. 28, No. 5 (Oct., 1991), pp. 1265-1281, Jstor.      
  36. The Taylor-Galerkin discontinuous finite element method-An explicit scheme for nonlinear hyperbolic conservation laws.
    Choe, K.Y.; Holsapple, K.A.
    Finite elements in analysis and design, 1991, vol. 10, no. 3, pp. 243, Ingenta.   
  37. Characteristic Galerkin Methods for Scalar Conservation Laws in One Dimension  
    P. N. Childs; K. W. Morton  
    SIAM Journal on Numerical Analysis > Vol. 27, No. 3 (Jun., 1990), pp. 553-594, Jstor.    
  38. A Subdomain-Galerkin/Least Squares Method for First-Order Elliptic Systems in the Plane  
    Ching-Lung Chang; Max D. Gunzburger  
    SIAM Journal on Numerical Analysis > Vol. 27, No. 5 (Oct., 1990), pp. 1197-1211, Jstor.     
  39. On spline approximation for a class of integral equations. I. Galerkin and collocation methods with piecewise polynomials.    
    Elschner, Johannes    
    Math. Methods Appl. Sci. 10 (1988), no. 5, 543--559, MathSciNet.  
  40. Convergence Analysis for a Nonsymmetric Galerkin Method for a Class of Singular Boundary Value Problems in One Space Dimension   
    Kenneth Eriksson, Yi-Yong Nie   
    Mathematics of Computation, Vol. 49, No. 179. (Jul., 1987), pp. 167-186, Jstor.  
  41. On the Galerkin and Collocation Methods for a Cauchy Singular Integral Equation   
    George Miel   
    SIAM Journal on Numerical Analysis, Vol. 23, No. 1. (Feb., 1986), pp. 135-143, Jstor.  
  42. The Performance of the Collocation and Galerkin Methods with Hermite Bi-Cubics   
    W. R. Dyksen, E. N. Houstis, R. E. Lynch, J. R. Rice   
    SIAM Journal on Numerical Analysis, Vol. 21, No. 4. (Aug., 1984), pp. 695-715, Jstor.  
  43. Galerkin Methods for Two-Point Boundary Value Problems for First Order Systems   
    William J. Layton   
    SIAM Journal on Numerical Analysis, Vol. 20, No. 1. (Feb., 1983), pp. 161-171, Jstor.  
  44. Discontinuous Galerkin Methods for Ordinary Differential Equations   
    M. Delfour, W. Hager, F. Trochu   
    Mathematics of Computation, Vol. 36, No. 154. (Apr., 1981), pp. 455-473, Jstor.  
  45. Discontinuous Galerkin methods for ordinary differential equations.
    Delfour, M.; Hager, W.; Trochu, F.
    Math. Comp. 36 (1981), no. 154, 455--473, MathSciNet.  
  46. A "Sinc-Galerkin" Method of Solution of Boundary Value Problems   
    Frank Stenger   
    Mathematics of Computation, Vol. 33, No. 145. (Jan., 1979), pp. 85-109, Jstor.  
  47. Uniform Convergence of Galerkin's Method for Splines on Highly Nonuniform Meshes  
    Frank Natterer  
    Mathematics of Computation, Vol. 31, No. 138. (Apr., 1977), pp. 457-468, Jstor.  
  48. A Collocation-Galerkin Method for the Two Point Boundary Value Problem Using Continuous Piecewise Polynomial Spaces   
    Julio Cesar Diaz   
    SIAM Journal on Numerical Analysis, Vol. 14, No. 5. (Sep., 1977), pp. 844-858, Jstor.  
  49. Some Collocation-Galerkin Methods for Two-Point Boundary Value Problems   
    Roderick J. Dunn, Jr., Mary Fanett Wheeler   
    SIAM Journal on Numerical Analysis, Vol. 13, No. 5. (Oct., 1976), pp. 720-733, Jstor.  
  50. A note on local Galerkin and collocation methods for ordinary differential equations.    
    Nørsett, Syvert P.    
    Utilitas Math. 7 (1975), 197--209, MathSciNet.  
  51. The Relation between the Galerkin and Collocation Methods Using Smooth Splines   
    Blair Swartz, Burton Wendroff   
    SIAM Journal on Numerical Analysis, Vol. 11, No. 5. (Oct., 1974), pp. 994-996, Jstor.  
  52. An Optimal Linf Error Estimate for Galerkin Approximations to Solutions of Two-Point Boundary Value Problems  
    Mary Fanett Wheeler  
    SIAM Journal on Numerical Analysis, Vol. 10, No. 5. (Oct., 1973), pp. 914-917, Jstor.  
  53. Discrete Galerkin and Related One-Step Methods for Ordinary Differential Equations   
    Bernie L. Hulme   
    Mathematics of Computation, Vol. 26, No. 120. (Oct., 1972), pp. 881-891, Jstor.  
  54. Galerkin Approximations and the Optimization of Difference Schemes for Boundary Value Problems  
    W. L. Miranker
    SIAM Journal on Numerical Analysis, Vol. 8, No. 3. (Sep., 1971), pp. 486-496, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2005