논문KCI 등재
An extrapolated Crank-Nicolson characteristic finite element method for Sobolev equations
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초록
We introduce an extrapolated Crank-Nicolson characteristic finite element method to approximate solutions of a convection dominated Sobolev equation. We obtain the higher order of convergence in both the spatial direction and the temporal direction in $L^{2}$ normed space for the extrapolated Crank-Nicolson characteristic finite element method.
Abstract
We introduce an extrapolated Crank-Nicolson characteristic finite element method to approximate solutions of a convection dominated Sobolev equation. We obtain the higher order of convergence in both the spatial direction and the temporal direction in $L^{2}$ normed space for the extrapolated Crank-Nicolson characteristic finite element method.
참고문헌 (23)
- D. N. Arnold, "Superconvergence of a finite element approximation to the solution of a Sobolev equation in a single space variable", Math. Comp, 36(153), pp.53~63 (1981)
- 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)
- R. W. Carroll, "Singular and degenerate Cauchy problems" (1976), Academic Press
- P. L. Davis, "A quasilinear parabolic and related third order problem", J. Math. Anal. Appl, 49, pp.327~335 (1970)
- 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(5), pp.871~885 (1982)
- R. E. Ewing, "Time-stepping Galerkin methods for nonlinear Sobolev partial differential equations", SIAM J. Numer. Anal, 15(6), pp.1125~1150 (1978)
- H. Gu, "Characteristic finite element methods for nonlinear Sobolev equations", Appl. Math. Comput, 102(1), pp.51~62 (1999)
- L. Guo, "H1-Galerkin mixed finite element method for the Sobolev equa-tion", J. Systems Sci. Math. Sci, 26(3), pp.301~314 (2006)
- H. Guo, "Least-squares Galerkin procedures for the Sobolev equations", Acta Math. Appl. Sin, 29(4), pp.609~618 (2006)
- Y. Lin, "Galerkin methods for nonlinear Sobolev equations", Aequationes Math, 40(1), pp.54~66 (1990)
- Y. Lin, "Finite element methods for nonlinear Sobolev equations with nonlinear boundary conditions", J. Math. Anal. Appl, 165(1), pp.180~191 (1992)
- 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)
- 엄미례, "L^2-error analysis of fully discrete discontinuous Galerkin approximations for nonlinear Sobolev equations", 대한수학회보, 48(5), pp.897~915 (2011), 대한수학회
- M. R. Ohm, "L2-error analysis of discontinuous Galerkin approximations for nonlinear Sobolev equations", Jpn. J. Ind. Appl. Math, 30(1), pp.91~110 (2013)
- 엄미례, "A CRANK-NICOLSON CHARACTERISTIC FINITE ELEMENT METHOD FOR SOBOLEV EQUATIONS", East Asian Mathematical Journal, 32(5), pp.729~744 (2016), 영남수학회[DOI]
- A. Pehlivanov, "Least-squares mixed finite elements for second-order elliptic problems", SIAM J. Numer. Anal, 31(5), pp.1368~1377 (1994)
- H. X. Rui, "A remark on least-squares mixed element methods for reaction-diffusion problems", J. Comput. Appl. Math, 202(2), pp.203~236 (2007)
- D. M. Shi, "The initial-boundary value problem for a nonlinear equation of migration of moisture in soil", Acta Math. Appl. Sinica, 13, pp.31~38 (1990)
- 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)
- 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)
- T. W. Ting, "A cooling process according to two-temperature theory of heat conduction", J. Math. Anal. Appl, 45, pp.23~31 (1974)
- D. P. Yang, "Some least-squares Galerkin procedures for first-order time-dependent convection-diffusion system", Comput. Methods Appl. Mech. Engrg, 108(1-2), pp.81~95 (1999)
- D. P. Yang, "Analysis of least-squares mixed finite element methods for nonlinear nonsta-tionary convection-diffusion problems", Math. Comp, 69(231), pp.929~963 (2000)
관련 논문AI추천
An Extrapolated Higher Order Characteristic Finite Element Method for Nonlinear Sobolev Equations신준용, 엄미례영남수학회 · East Asian Mathematical Journal2018 · 제34권 제5호A CRANK-NICOLSON CHARACTERISTIC FINITE ELEMENT METHOD FOR SOBOLEV EQUATIONS신준용, 엄미례영남수학회 · East Asian Mathematical Journal2016 · 제32권 제5호A CRANK-NICOLSON CHARACTERISTIC FINITE ELEMENT METHOD FOR NONLINEAR SOBOLEV EQUATIONS신준용, 엄미례영남수학회 · East Asian Mathematical Journal2017 · 제33권 제3호AN EXTRAPOLATED HIGHER ORDER CHARACTERISTIC FINITE ELEMENT METHOD FOR SOBOLEV EQUATIONS신준용, 엄미례영남수학회 · East Asian Mathematical Journal2017 · 제33권 제5호A HIGHER ORDER SPLIT LEAST-SQUARES CHARACTERISTIC MIXED ELEMENT METHOD FOR SOBOLEV EQUATIONS신준용, 엄미례영남수학회 · East Asian Mathematical Journal2022 · 제38권 제3호A SPLIT LEAST-SQUARES CHARACTERISTIC MIXED ELEMENT METHOD FOR SOBOLEV EQUATIONS WITH A CONVECTION TERM신준용, 엄미례영남수학회 · East Asian Mathematical Journal2019 · 제35권 제5호
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