본문 바로가기
KERD
논문KCI 등재

An Extrapolated Higher Order Characteristic Finite Element Method for Nonlinear Sobolev Equations

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

주제분류수학

초록

Inthispaper,weintroduceanextrapolatedhigherorderchar- acteristic finite element method to approximate solutions of nonlinear Sobolev equations with a convection term and we establish the higher or- der of convergence in the temporal and the spatial directions with respect to L2 norm.

Abstract

Inthispaper,weintroduceanextrapolatedhigherorderchar- acteristic finite element method to approximate solutions of nonlinear Sobolev equations with a convection term and we establish the higher or- der of convergence in the temporal and the spatial directions with respect to L2 norm.

참고문헌 (28)

  1. 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)[DOI]
  2. G. I. Barenblatt, "Basic conception in the theory of seepage of homogenous liquids in fissured rocks", J. Appl. Math. Mech., 24, pp.1286~1309 (1960)[DOI]
  3. R. W. Carroll, "Singular and degenerate Cauchy problems (Mathematics in Sciences and Engineering, Vol. 127)" (1976), Academic Press
  4. P. L. Davis, "A quasilinear parabolic and related third order problem", J. Math. Anal. Appl., 49, pp.327~335 (1970)
  5. J. Douglas, "Numerical methods for convection-dominated diffusion problems based on combining the method of characteristic with finite element or finite difference procedures", SIAM J. Numer. Anal., 19, pp.871~885 (1982)[DOI]
  6. R. E. Ewing, "Time-stepping Galerkin methods for nonlinear Sobolev partial differential equations", SIAM J. Numer. Anal., 15, pp.1125~1150 (1978)[DOI]
  7. H. Gu, "Characteristic finite element methods for nonlinear Sobolev equations", Applied Math. Compu., 102, pp.51~62 (1999)
  8. L. Guo, "<TEX>$H^1$<", TEX>-Galerkin mixed finite element method for the Sobolev equation, 2006, pp.26, 301~314
  9. H. Guo, "Least-squares Galerkin mixed finite element method for the Sobolev equation", Acta Math. Appl. Sinica, 29, pp.609~618 (2006)
  10. Y. Lin, "Galerkin methods for nonlinear Sobolev equations", Aequationes Mathematicae, 40, pp.54~66 (1990)[DOI]
  11. Y. Lin, "Finite element methods for nonlinear Sobolev equations with nonlinear boundary conditions", Journal of Math. Anal. and Appl., 165, pp.180~191 (1992)[DOI]
  12. M. T. Nakao, "Error estimates of a Galerkin method for some nonlinear Sobolev equations in one space dimension", Numer. Math., 47, pp.139~157 (1985)[DOI]
  13. 엄미례, "L^2-error analysis of fully discrete discontinuous Galerkin approximations for nonlinear Sobolev equations", 대한수학회보, 48(5), pp.897~915 (2011), 대한수학회
  14. M. R. Ohm, "<TEX>$L^2$<", TEX>-error analysis of discontinuous Galerkin approximations for nonlinear Sobolev equations, 2013, pp.30(1), 91~110
  15. 엄미례, "A CRANK-NICOLSON CHARACTERISTIC FINITE ELEMENT METHOD FOR SOBOLEV EQUATIONS", East Asian Mathematical Journal, 32(5), pp.729~744 (2016), 영남수학회[DOI]
  16. 엄미례, "A CRANK-NICOLSON CHARACTERISTIC FINITE ELEMENT METHOD FOR NONLINEAR SOBOLEV EQUATIONS", East Asian Mathematical Journal, 33(3), pp.295~308 (2017), 영남수학회
  17. 엄미례, "An extrapolated Crank-Nicolson characteristic finite element method for Sobolev equations", 대한수학회보, 54(4), pp.1409~1419 (2017), 대한수학회
  18. 엄미례, "AN EXTRAPOLATED HIGHER ORDER CHARACTERISTIC FINITE ELEMENT METHOD FOR SOBOLEV EQUATIONS", East Asian Mathematical Journal, 33(5), pp.511~525 (2017), 영남수학회[DOI]
  19. 엄미례, "AN EXTRAPOLATED CRANK-NICOLSON CHARACTERISTIC FINITE ELEMENT METHOD FOR NONLINEAR SOBOLEV EQUATIONS", Journal of Applied Mathematics and Informatics, 36(3), pp.257~270 (2018), 한국전산응용수학회[DOI]
  20. A. Pehlivanov, "Least-squares mixed finite elements for second-order elliptic problems", SIAM J. Numer. Anal., 31, pp.1368~1377 (1994)[DOI]
  21. H. X. Rui, "A remark on least-squares mixed element methods for reaction-diffusion problems", J. Comput. Appl. Math., 202, pp.203~236 (2007)[DOI]
  22. D. Shi, "A lower order characteristic-nonconforming finite element method for nonlinear Sobolev equation with convection-dominated term", Math. Comput. Simulation, 114, pp.25~36 (2015)[DOI]
  23. D. M. Shi, "On the initial boundary value problem of nonlinear the equation of the migration of the moisture in soil", Acta math. Appl. Sinica, 13, pp.31~38 (1990)
  24. T. Sun, "A priori error estimates for interior penalty discontinuous Galerkin method applied to nonlinear Sobolev equations", Appl. Math. and Comput., 200, pp.147~159 (2008)
  25. T. Sun, "Error estimates for a discontinuous Galerkin method with interior penalties applied to nonlinear Sobolev equations", Numer. Meth. Part. Differ. Equa., 24(3), pp.879~896 (2008)[DOI]
  26. T. W. Ting, "A cooling process according to two-temperature theory of heat conduction", J. Math. Anal. Appl., 45, pp.23~31 (1974)[DOI]
  27. D. P. Yang, "Some least-squares Galerkin procedures for first-order time-dependent convection-diffusion system", Comput. Methods Appl. Mech. Eng., 108, pp.81~95 (1999)
  28. D. P. Yang, "Analysis of least-squares mixed finite element methods for nonlinear nonstationary convection-diffusion problems", Math. Comput., 69, pp.929~963 (2000)

관련 논문AI추천

이 간행물의 다른 논문 (14건)