논문KCI 등재
A CRANK-NICOLSON CHARACTERISTIC FINITE ELEMENT METHOD FOR SOBOLEV EQUATIONS
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참고문헌
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주제분류수학
초록
A Crank-Nicolson characteristic finite element method is in troduced to construct approximate solutions of a Sobolev equation with a convection term. The higher order of convergences in the temporal direction and in the spatial direction in L2 normed space are verified for the Crank-Nicolson characteristic finite element method.
Abstract
A Crank-Nicolson characteristic finite element method is in troduced to construct approximate solutions of a Sobolev equation with a convection term. The higher order of convergences in the temporal direction and in the spatial direction in L2 normed space are verified for the Crank-Nicolson characteristic finite element method.
참고문헌 (22)
- 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)
- 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, pp.871~885 (1982)
- R. E. Ewing, "Time-stepping Galerkin methods for nonlinear Sobolev partial differential equations", SIAM J. Numer. Anal., 15, pp.1125~1150 (1978)
- H. Gu, "Characteristic finite element methods for nonlinear Sobolev equations", Applied Math. Compu, 102, pp.51~62 (1999)
- L. Guo, "H1-Galerkin mixed finite element method for the Sobolev equation", J. Sys. Sci., 26, pp.301~314 (2006)
- H. Guo, "Least-squares Galerkin mixed finite element method for the Sobolev equation", Acta Math. Appl. Sinica, 29, pp.609~618 (2006)
- Y. Lin, "Galerkin methods for nonlinear Sobolev equations", Aequationes Mathematicae, 40, pp.54~66 (1990)
- Y. Lin, "Finite element methods for nonlinear Sobolev equations with nonlinear boundary conditions", Journal of Math. Anal. and Appl, 165, pp.180~191 (1992)
- 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)
- 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 approx-imations for nonlinear Sobolev equations", J. Japanese Indus. Appl. Math., 30(1), pp.91~110 (2013)
- A. Pehlivanov, "Least-squares mixed finite elements for second-order elliptic problems", SIAM J. Numer. Anal., 31, pp.1368~1377 (1994)
- H. X. Rui, "A remark on least-squares mixed element methods for reaction-diffusion problems", J. Comput. Appl. Math., 202, pp.203~236 (2007)
- 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)
- 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)
- 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)
- 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. Eng., 108, pp.81~95 (1999)
- D. P. Yang, "Analysis of least-squares mixed finite element methods for nonlinear non-stationary convection-diffusion problems", Math. Comput., 69, pp.929~929 (2000)
관련 논문AI추천
A CRANK-NICOLSON CHARACTERISTIC FINITE ELEMENT METHOD FOR NONLINEAR SOBOLEV EQUATIONS신준용, 엄미례영남수학회 · East Asian Mathematical Journal2017 · 제33권 제3호An extrapolated Crank-Nicolson characteristic finite element method for Sobolev equations신준용, 엄미례대한수학회 · 대한수학회보2017 · 제54권 제4호AN EXTRAPOLATED HIGHER ORDER CHARACTERISTIC FINITE ELEMENT METHOD FOR SOBOLEV EQUATIONS신준용, 엄미례영남수학회 · East Asian Mathematical Journal2017 · 제33권 제5호An Extrapolated Higher Order Characteristic Finite Element Method for Nonlinear Sobolev Equations신준용, 엄미례영남수학회 · East Asian Mathematical Journal2018 · 제34권 제5호A SPLIT LEAST-SQUARES CHARACTERISTIC MIXED ELEMENT METHOD FOR SOBOLEV EQUATIONS WITH A CONVECTION TERM신준용, 엄미례영남수학회 · East Asian Mathematical Journal2019 · 제35권 제5호A HIGHER ORDER SPLIT LEAST-SQUARES CHARACTERISTIC MIXED ELEMENT METHOD FOR SOBOLEV EQUATIONS신준용, 엄미례영남수학회 · East Asian Mathematical Journal2022 · 제38권 제3호
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