L^2-error analysis of fully discrete discontinuous Galerkin approximations for nonlinear Sobolev equations

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참고문헌 (21)

1. D. N. Arnold, "An interior penalty finite element method with discontinuous elements", SIAM J. Numer. Anal, 19(4), pp.724~760 (1982)
2. D. N. Arnold, "Superconvergence of a finite approximation to the solution of a Sobolev equation in a single space variable", Math. Comp, 36, pp.53~63 (1981)
3. I. Babuska, "The h-p version of the finite element method with quasi-uniform meshes", RAIRO Model. Math. Anal. Num, 21(2), pp.199~238 (1987)
4. I. Babuska, "The optimal convergence rates of the p-version of the finite element method", SIAM J. Numer. Anal, 24(4), pp.750~776 (1987)
5. G. I. Barenblatt, "Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks", J. Appl. Math. Mech, 23, pp.1286~1303 (1960)
6. R. W. Carroll, "Singular and Degenerate Cauchy Problems", Math- ematics in Sciences and Engineering, 127 (1976), Academic Press
7. P. J. Chen, "On a theory of heat conduction involving two temperatures", Z. Angew Math. Phys, pp.614~627 (1968)
8. P. L. Davis, "A quasilinear parabolic and a related third order problem", J. Math. Anal. Appl, 40, pp.327~335 (1972)
9. R. E. Ewing, "The approximation of certain parabolic equations backward in time by Sobolev equations", SIAM J. Math. Anal, 6, pp.283~294 (1975)
10. R. E. Ewing, "Time-stepping Galerkin methods for nonlinear Sobolev partial differential equa- tions", SIAM J. Numer. Anal, 15(6), pp.1125~1150 (1978)
11. W. H. Ford, "Stability and convergence of difference approximations to pseudo-parabolic partial differential equations", Math. Comput, 27, pp.737~743 (1973)
12. W. H. Ford, "Uniform error estimates for difference approximations to nonlinear pseudo- parabolic partial differential equations", SIAM J. Numer. Anal, 11, pp.155~169 (1974)
13. Y. Lin, "Galerkin methods for nonlinear Sobolev equations", Aequationes Math, 40(1), pp.54~66 (1990)
14. Y. Lin, "Finite element methods for nonlinear Sobolev equations with nonlinear boundary conditions", J. Math. Anal. Appl, 165(1), pp.180~191 (1992)
15. M. T. Nakao, "Error estimates of a Galerkin method for some nonlinear Sobolev equa- tions in one space dimension", Numer. Math, 47(1), pp.139~157 (1985)
16. M. R. Ohm, "Error estimates for discontinuous Galerkinmethod for nonlinear parabolic equations", J. Math. Anal. Appl, 315(1), pp.132~143 (2006)
17. M. R. Ohm, "L2-error analysis of discontinuous Galerkin approximations for nonlinear Sobolev equations"
18. T. Sun, "A priori error estimates for interior penalty discontinuous Galerkin method applied to nonlinear Sobolev equations", Appl. Math. Comput, 200(1), pp.147~159 (2008)
19. T. Sun, "Error estimates for a discontinuous Galerkin method with interior penalties applied to nonlinear Sobolev equations", Numer. Methods Partial Differential Equations, 24(3), pp.879~896 (2008)
20. T. W. Ting, "A cooling process according to two-temperature theory of heat conduction", J. Math. Anal. Appl, 45, pp.289~303 (1974)
21. M. F. Wheeler, "A priori L2 error estimates for Galerkin approximations to parabolic partial differential equations", SIAM J. Numer. Anal, 10, pp.723~759 (1973)

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