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Section B

Mixed discontinuous Legendre wavelet Galerkin method for solving elliptic partial differential equations

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Pages 3626-3645 | Received 01 Apr 2011, Accepted 30 Jul 2011, Published online: 19 Sep 2011

References

  • Alpert , B. 1993 . A class of bases in L2 for the sparse representation of integral operators . SIAM J. Math. Anal , 24 : 247 – 262 .
  • Alpert , B. , Beylkin , G. , Gines , D. and Vozovoi , L. 2002 . Adaptive solution partial differential equations in multiwavelet bases . J. Comp. Phys , 182 : 149 – 190 .
  • Arnold , D. , Brezzi , F. , Cockburn , B. and Marini , D. 2001 . Unified analysis of discontinuous Galerkin methods for elliptic problems . SIAM J. Numer. Anal , 39 : 1749 – 1779 .
  • Berlkin , G. 1992 . On the representation of operators in bases of compactly supported wavelets . SIAM J. Numer. Anal , 6 : 1716 – 1739 .
  • Beylkin , G. , Garcke , J. and Mohlenkamp , M. J. 2009 . Multivariate regression and machine learning with sum of separable functions . SIAM J. Sci. Comput , 3 : 1840 – 1857 .
  • Cockburn , B. 2001 . Devising discontinuous Galerkin methods for nonlinear hyperbolic conservation laws . J. Comput. Appl. Math , 128 : 187 – 190 .
  • Cockburn , B. , Kanschat , G. , Schotzau , D. and Schwab , C. 2002 . Local discontinuous Galerkin methods for the Stokes system . SIAM J. Numer. Anal , 40 ( 1 ) : 337 – 343 .
  • Cockburn , B. , Gopalakrishnan , J. and Lazarov , R. 2009 . Unified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems . SIAM J. Numer. Anal , 47 : 1319 – 1365 .
  • Dahmen , W. , Kurdila , J. and Oswald , P. 1997 . Multiscale Wavelet Methods for Partial Differential Equations , San Diego, CA : Academic Press .
  • Frohlichand , J. and Schneider , K. 1997 . An adaptive-vaguelette algorithm for the solution of PDEs . J. Comput. Phys , 130 : 174 – 190 .
  • Gantumur , T. and Stevenson , R. 2006 . Computation of differential operators in wavelet coordinates . Math. Comp , 75 : 697 – 709 .
  • Kumar , R. B.V. and Mehra , M. 2006 . A three-step wavelet Galerkin method for parabolic and hyperbolic partial differential equations . Int. J. Comput. Math , 83 : 143 – 157 .
  • Liandrat , J. , Perrier , V. and Tchamitchian , P. 1992 . Numerical resolution of nonlinear partial differential equations using wavelet approach . Wavelets Appl , : 227 – 238 .
  • Quarteroni , A. and Valli , A. 1997 . Numerical Approximation of Partial Differential Equations , Berlin : Springer-Verlag .
  • Razzaghi , M. and Yousefl , S. 2000 . Legendre wavelets direct method for variational problems . Math. Comput. Simulation , 53 : 190 – 199 .
  • Razzaghi , M. and Yousefi , S. 2001 . The Legendre wavelets operational matrix of integration . Internat. J. Systems Sci , 32 : 500 – 502 .
  • Reed , W. H. and Hill , T. R. 1973 . Triangular mesh methods for the neutron transport equation , Los Alamos Science Laboratory . Tech. Rep. LA-UR-73-479
  • Wazwaz , M. 2002 . A new method for solving singular initial value problems in the second-order ordinary differential equations . Appl. Math. Comput , 128 : 45 – 57 .
  • Yousefi , S. 2010 . Legendre multiwavelet Galerkin method for solving the hyperbolic telegraph equation . Numer. Methods Partial Differential Equations , 26 ( 3 ) : 539 – 543 .
  • Zheng , X. Y. and Yang , X. F. 2009 . Techniques for solving integral and differential equations by Legendre wavelets . Internat. J. Systems Sci , 11 : 1127 – 1137 .

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