논문KCI 등재
An Extrapolated Higher Order Characteristic Finite Element Method for Nonlinear Sobolev Equations
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참고문헌
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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)
- 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]
- 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]
- R. W. Carroll, "Singular and degenerate Cauchy problems (Mathematics in Sciences and Engineering, Vol. 127)" (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)[DOI]
- R. E. Ewing, "Time-stepping Galerkin methods for nonlinear Sobolev partial differential equations", SIAM J. Numer. Anal., 15, pp.1125~1150 (1978)[DOI]
- H. Gu, "Characteristic finite element methods for nonlinear Sobolev equations", Applied Math. Compu., 102, pp.51~62 (1999)
- L. Guo, "<TEX>$H^1$<", TEX>-Galerkin mixed finite element method for the Sobolev equation, 2006, pp.26, 301~314
- 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)[DOI]
- 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]
- 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]
- 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, "<TEX>$L^2$<", TEX>-error analysis of discontinuous Galerkin approximations for nonlinear Sobolev equations, 2013, pp.30(1), 91~110
- 엄미례, "A CRANK-NICOLSON CHARACTERISTIC FINITE ELEMENT METHOD FOR SOBOLEV EQUATIONS", East Asian Mathematical Journal, 32(5), pp.729~744 (2016), 영남수학회[DOI]
- 엄미례, "A CRANK-NICOLSON CHARACTERISTIC FINITE ELEMENT METHOD FOR NONLINEAR SOBOLEV EQUATIONS", East Asian Mathematical Journal, 33(3), pp.295~308 (2017), 영남수학회
- 엄미례, "An extrapolated Crank-Nicolson characteristic finite element method for Sobolev equations", 대한수학회보, 54(4), pp.1409~1419 (2017), 대한수학회
- 엄미례, "AN EXTRAPOLATED HIGHER ORDER CHARACTERISTIC FINITE ELEMENT METHOD FOR SOBOLEV EQUATIONS", East Asian Mathematical Journal, 33(5), pp.511~525 (2017), 영남수학회[DOI]
- 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]
- A. Pehlivanov, "Least-squares mixed finite elements for second-order elliptic problems", SIAM J. Numer. Anal., 31, pp.1368~1377 (1994)[DOI]
- 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]
- 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]
- 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)[DOI]
- T. W. Ting, "A cooling process according to two-temperature theory of heat conduction", J. Math. Anal. Appl., 45, pp.23~31 (1974)[DOI]
- 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 nonstationary convection-diffusion problems", Math. Comput., 69, pp.929~963 (2000)
관련 논문AI추천
AN EXTRAPOLATED HIGHER ORDER CHARACTERISTIC FINITE ELEMENT METHOD FOR SOBOLEV EQUATIONS신준용, 엄미례영남수학회 · East Asian Mathematical Journal2017 · 제33권 제5호An extrapolated Crank-Nicolson characteristic finite element method for Sobolev equations신준용, 엄미례대한수학회 · 대한수학회보2017 · 제54권 제4호A CRANK-NICOLSON CHARACTERISTIC FINITE ELEMENT METHOD FOR NONLINEAR SOBOLEV EQUATIONS신준용, 엄미례영남수학회 · East Asian Mathematical Journal2017 · 제33권 제3호A CRANK-NICOLSON CHARACTERISTIC FINITE ELEMENT METHOD FOR SOBOLEV EQUATIONS신준용, 엄미례영남수학회 · East Asian Mathematical Journal2016 · 제32권 제5호A HIGHER ORDER SPLIT LEAST-SQUARES CHARACTERISTIC MIXED ELEMENT METHOD FOR SOBOLEV EQUATIONS신준용, 엄미례영남수학회 · East Asian Mathematical Journal2022 · 제38권 제3호Extrapolated Expanded Mixed Finite Element Approximations of Semilinear Sobolev Equations신준용, 엄미례, 이현영영남수학회 · East Asian Mathematical Journal2014 · 제30권 제3호
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