References
- A. K. Aziz, R. B. Kellogg, and A. B. Stephens, Least squares methods for elliptic systems, Math. Comp. 44 (1985), no. 169, 53-70. https://doi.org/10.1090/S0025-5718-1985-0771030-5
- C. Bernardi and Y. Maday, Approximations spectrales de problemes aux limites ellip-tiques, vol. 10 of Mathematiques & Applications (Berlin) [Mathematics & Applications], Springer-Verlag, Paris, 1992.
- M. Berndt, T. A. Manteuffel, and S. F. McCormick, Analysis of first-order system least squares (FOSLS) for elliptic problems with discontinuous coefficients. II, SIAM J. Numer. Anal. 43 (2005), no. 1, 409-436 (electronic). https://doi.org/10.1137/S003614290342769X
- M. Berndt, T. A. Manteuffel, S. F. McCormick, and G. Starke, Analysis of first-order system least squares (FOSLS) for elliptic problems with discontinuous coefficients. I, SIAM J. Numer. Anal. 43 (2005), no. 1, 386-408. https://doi.org/10.1137/S0036142903427688
- P. B. Bochev and M. D. Gunzburger, Analysis of least squares finite element methods for the Stokes equations, Math. Comp. 63 (1994), no. 208, 479-506. https://doi.org/10.1090/S0025-5718-1994-1257573-4
- P. B. Bochev and M. D. Gunzburger, Finite element methods of least-squares type, SIAM Rev. 40 (1998), no. 4, 789-837. https://doi.org/10.1137/S0036144597321156
- P. Boomkamp, B. Boersma, R. Miesen, and G. Beijnon, A chebyshev collocation method for solving two-phase flow stability problems, J. Comput. Phys. 132 (1997), 191-200. https://doi.org/10.1006/jcph.1996.5571
- J. H. Bramble, R. D. Lazarov, and J. E. Pasciak, A least-squares approach based on a discrete minus one inner product for first order systems, Math. Comp. 66 (1997), no. 219, 935-955. https://doi.org/10.1090/S0025-5718-97-00848-X
- Z. Cai, R. Lazarov, T. A. Manteuffel, and S. F. McCormick, First-order system least squares for second-order partial differential equations. I, SIAM J. Numer. Anal. 31 (1994), no. 6, 1785-1799. https://doi.org/10.1137/0731091
- Z. Cai, T. A. Manteuffel, and S. F. McCormick, First-order system least squares for second-order partial differential equations. II, SIAM J. Numer. Anal. 34 (1997), no. 2, 425-454. https://doi.org/10.1137/S0036142994266066
- Z. Cai and B. C. Shin, The discrete first-order system least squares: the second-order elliptic boundary value problem, SIAM J. Numer. Anal. 40 (2002), no. 1, 307-318 (electronic). https://doi.org/10.1137/S0036142900381886
- C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods in Fluid Dynamics, Springer Series in Computational Physics, Springer-Verlag, New York, 1988.
- Y. Cao and M. D. Gunzburger, Least-squares finite element approximations to solutions of interface problems, SIAM J. Numer. Anal. 35 (1998), no. 1, 393-405 (electronic). https://doi.org/10.1137/S0036142996303249
- G. J. Fix, M. D. Gunzburger, and R. A. Nicolaides, On finite element methods of the least squares type, Comput. Math. Appl. 5 (1979), no. 2, 87-98. https://doi.org/10.1016/0898-1221(79)90062-2
- G. J. Fix and E. Stephan, On the finite element-least squares approximation to higher order elliptic systems, Arch. Rational Mech. Anal. 91 (1985), no. 2, 137-151.
- D. Funaro, A variational formulation for the Chebyshev pseudospectral approximation of Neumann problems, SIAM J. Numer. Anal. 27 (1990), no. 3, 695-703. https://doi.org/10.1137/0727041
- D. Jesperson, A least squares decomposition method for solving elliptic equations, Math. Comp. 31 (1977), no. 140, 873-880. https://doi.org/10.1090/S0025-5718-1977-0461948-0
- B.-N. Jiang, The Least-Squares Finite Element Method, Springer-Verlag, Berlin, 1998.
- J.-H. Jung, A note on the spectral collocation approximation of some differential equa- tions with singular source terms, J. Sci. Comput. 39 (2009), no. 1, 49-66. https://doi.org/10.1007/s10915-008-9249-x
- S. D. Kim, H.-C. Lee, and B. C. Shin, Pseudospectral least-squares method for the second-order elliptic boundary value problem, SIAM J. Numer. Anal. 41 (2003), no. 4, 1370-1387 (electronic). https://doi.org/10.1137/S0036142901398234
- S. D. Kim, H.-C. Lee, and B. C. Shin, Least-squares spectral collocation method for the Stokes equations, Numer. Methods Partial Differential Equations 20 (2004), no. 1, 128-139. https://doi.org/10.1002/num.10085
- S. D. Kim and B. C. Shin, Chebyshev weighted norm least-squares spectral methods for the elliptic problem, J. Comput. Math. 24 (2006), no. 4, 451-462.
- A. Loubenets, T. Ali, and M. Hanke, Highly accurate finite element method for one- dimensional elliptic interface problems, Appl. Numer. Math. 59 (2009), no. 1, 119-134. https://doi.org/10.1016/j.apnum.2007.12.003
- A. I. Pehlivanov, G. F. Carey, and R. D. Lazarov, Least-squares mixed finite elements for second-order elliptic problems, SIAM J. Numer. Anal. 31 (1994), no. 5, 1368-1377. https://doi.org/10.1137/0731071
- M. M. J. Proot and M. I. Gerritsma, A least-squares spectral element formulation for the Stokes problem, J. Sci. Comput. 17 (2002), no. 1-4, 285-296. https://doi.org/10.1023/A:1015121219065
- A. Quarteroni and A. Valli, Numerical Approximation of Partial Differential Equations, vol. 23 of Springer Series in Computational Mathematics, Springer-Verlag, Berlin, 1994.
- Z. G. Seftel, A general theory of boundary value problems for elliptic systems with discontinuous coefficients, Ukrain. Mat. Z. 18 (1966), no. 3, 132-136. https://doi.org/10.1007/BF02537868
- B.-C. Shin and J.-H. Jung, Spectral collocation and radial basis function methods for one-dimensional interface problems, Appl. Numer. Math. 61 (2011), no. 8, 911-928. https://doi.org/10.1016/j.apnum.2011.03.005
- A.-K. Tornberg and B. Engquist, Numerical approximations of singular source terms in differential equations, J. Comput. Phys. 200 (2004), no. 2, 462-488. https://doi.org/10.1016/j.jcp.2004.04.011