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Volumn 200, Issue 1, 2008, Pages 147-159

A priori error estimates for interior penalty discontinuous Galerkin method applied to nonlinear Sobolev equations

Author keywords

Discontinuous Galerkin method; Error estimates; Interior penalty; Nonlinear Sobolev equations

Indexed keywords

ERROR ANALYSIS; NONLINEAR EQUATIONS; PROBLEM SOLVING;

EID: 43049183328     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2007.10.053     Document Type: Article
Times cited : (29)

References (24)
  • 1
    • 0027641889 scopus 로고
    • Discontinuous Galerkin finite element methods for second order hyperbolic problems
    • Johnson C. Discontinuous Galerkin finite element methods for second order hyperbolic problems. Comput. Methods Appl. Mech. Eng. 107 (1993) 117-129
    • (1993) Comput. Methods Appl. Mech. Eng. , vol.107 , pp. 117-129
    • Johnson, C.1
  • 2
    • 0035382415 scopus 로고    scopus 로고
    • A priori error estimates for finite element methods based on discontinuous approximation spaces for elliptic problems
    • Rivière B., Wheeler M.F., and Girault V. A priori error estimates for finite element methods based on discontinuous approximation spaces for elliptic problems. SIAM J. Numer. Anal. 39 3 (2001) 902-931
    • (2001) SIAM J. Numer. Anal. , vol.39 , Issue.3 , pp. 902-931
    • Rivière, B.1    Wheeler, M.F.2    Girault, V.3
  • 3
    • 0037073026 scopus 로고    scopus 로고
    • Discontinuous and coupled continuous/discontinuous Galerkin methods for the shallow water equations
    • Dawson C., and Proft J. Discontinuous and coupled continuous/discontinuous Galerkin methods for the shallow water equations. Comput. Methods Appl. Mech. Eng. 191 (2002) 4721-4746
    • (2002) Comput. Methods Appl. Mech. Eng. , vol.191 , pp. 4721-4746
    • Dawson, C.1    Proft, J.2
  • 4
    • 84904152686 scopus 로고
    • Finite element methods for elliptic equations using nonconforming elements
    • Baker G. Finite element methods for elliptic equations using nonconforming elements. Math. Comput. 31 (1977) 45-59
    • (1977) Math. Comput. , vol.31 , pp. 45-59
    • Baker, G.1
  • 5
    • 0001456343 scopus 로고
    • Interior penalty procedures for elliptic and parabolic Galerkin methods
    • Douglas Jr. J., and Dupont T. Interior penalty procedures for elliptic and parabolic Galerkin methods. Lect. Notes Phys. 58 (1976) 207-216
    • (1976) Lect. Notes Phys. , vol.58 , pp. 207-216
    • Douglas Jr., J.1    Dupont, T.2
  • 6
    • 0000802762 scopus 로고
    • An elliptic collocation-finite element method with interior penalties
    • Wheeler M.F. An elliptic collocation-finite element method with interior penalties. SIAM J. Numer. Anal. 15 (1978) 152-161
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 152-161
    • Wheeler, M.F.1
  • 7
    • 0001163226 scopus 로고
    • An interior penalty finite element method with discontinuous elements
    • Arnold D.N. An interior penalty finite element method with discontinuous elements. SIAM J. Numer. Anal. 19 (1982) 724-760
    • (1982) SIAM J. Numer. Anal. , vol.19 , pp. 724-760
    • Arnold, D.N.1
  • 8
    • 84951671794 scopus 로고
    • Über ein Variationspringzip zur Lösung von Drichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind
    • Nitsche J.A. Über ein Variationspringzip zur Lösung von Drichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. Abh. Math. Sem. Hamburg. 36 (1971) 9-15
    • (1971) Abh. Math. Sem. Hamburg. , vol.36 , pp. 9-15
    • Nitsche, J.A.1
  • 10
    • 0033511173 scopus 로고    scopus 로고
    • Part I. Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems
    • Rivière B., Wheeler M.F., and Girault V. Part I. Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. Comput. Geosci. 8 (1999) 337-360
    • (1999) Comput. Geosci. , vol.8 , pp. 337-360
    • Rivière, B.1    Wheeler, M.F.2    Girault, V.3
  • 11
    • 0343831462 scopus 로고    scopus 로고
    • Part II. Discontinuous Galerkin method applied to single phase flow in porous media
    • Rivière B., Wheeler M.F., and Banas K. Part II. Discontinuous Galerkin method applied to single phase flow in porous media. Comput. Geosci. 4 4 (2000) 337-341
    • (2000) Comput. Geosci. , vol.4 , Issue.4 , pp. 337-341
    • Rivière, B.1    Wheeler, M.F.2    Banas, K.3
  • 12
    • 0035382415 scopus 로고    scopus 로고
    • A priori error estimates for finite element methods based on discontinuous approximation spaces for elliptic problems
    • Rivière B., Wheeler M.F., and Girault V. A priori error estimates for finite element methods based on discontinuous approximation spaces for elliptic problems. SIAM J. Numer. Anal. 39 3 (2001) 902-931
    • (2001) SIAM J. Numer. Anal. , vol.39 , Issue.3 , pp. 902-931
    • Rivière, B.1    Wheeler, M.F.2    Girault, V.3
  • 13
    • 36248938881 scopus 로고
    • Basic concepts in the theory of seepage of homogenous liquids in fissured rocks
    • Barenblatt G.I., Zheltov I.P., and Kochina I.N. Basic concepts in the theory of seepage of homogenous liquids in fissured rocks. J. Appl. Math. Mech. 24 (1960) 1286-1303
    • (1960) J. Appl. Math. Mech. , vol.24 , pp. 1286-1303
    • Barenblatt, G.I.1    Zheltov, I.P.2    Kochina, I.N.3
  • 14
    • 0000949743 scopus 로고
    • On a theory of heat conduction involving two temperatures
    • Chen P.J., and Gurtin M.E. On a theory of heat conduction involving two temperatures. Z. Angew. Math. Phys. 19 (1968) 614-627
    • (1968) Z. Angew. Math. Phys. , vol.19 , pp. 614-627
    • Chen, P.J.1    Gurtin, M.E.2
  • 15
    • 0016518642 scopus 로고
    • Numerical solution of Sobolev partial differential equations
    • Ewing R.E. Numerical solution of Sobolev partial differential equations. SIAM J. Numer. Anal. 12 (1975) 345-363
    • (1975) SIAM J. Numer. Anal. , vol.12 , pp. 345-363
    • Ewing, R.E.1
  • 16
    • 0011412428 scopus 로고
    • Time-stepping Galerkin methods for nonlinear Sobolev partial differential equations
    • Ewing R.E. Time-stepping Galerkin methods for nonlinear Sobolev partial differential equations. SIAM J. Numer. Anal. 15 (1978) 1125-1150
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 1125-1150
    • Ewing, R.E.1
  • 17
    • 84978984527 scopus 로고    scopus 로고
    • Streamline-diffusion FEM for Sobolev equation with convection-dominated term
    • Sun T.J. Streamline-diffusion FEM for Sobolev equation with convection-dominated term. Appl. Math., J. Chinese Univ., Engl. Ser. 16 (2001) 63-71
    • (2001) Appl. Math., J. Chinese Univ., Engl. Ser. , vol.16 , pp. 63-71
    • Sun, T.J.1
  • 18
    • 0037168942 scopus 로고    scopus 로고
    • The finite element difference streamline-diffusion methods for Sobolev equation with convection-dominated term
    • Sun T.J., and Yang D.P. The finite element difference streamline-diffusion methods for Sobolev equation with convection-dominated term. Appl. Math. Comput. 125 (2002) 325-345
    • (2002) Appl. Math. Comput. , vol.125 , pp. 325-345
    • Sun, T.J.1    Yang, D.P.2
  • 19
    • 0000564951 scopus 로고
    • Total-variation-diminishing time discretizations
    • Shu C.-W. Total-variation-diminishing time discretizations. SIAM J. Sci. Stat. Comput. 9 6 (1988) 1073-1084
    • (1988) SIAM J. Sci. Stat. Comput. , vol.9 , Issue.6 , pp. 1073-1084
    • Shu, C.-W.1
  • 20
    • 84966246413 scopus 로고
    • TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: General framework
    • Cockburn B., and Shu C.-W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: General framework. Math. Comput. 52 186 (1989) 411-435
    • (1989) Math. Comput. , vol.52 , Issue.186 , pp. 411-435
    • Cockburn, B.1    Shu, C.-W.2
  • 21
    • 0000026672 scopus 로고
    • The h-p version of the finite element method with quasi-uniform meshes, RAIRO Modél
    • Babuška I., and Suri M. The h-p version of the finite element method with quasi-uniform meshes, RAIRO Modél. Math. Anal. Numer. 21 (1987) 199-238
    • (1987) Math. Anal. Numer. , vol.21 , pp. 199-238
    • Babuška, I.1    Suri, M.2
  • 22
    • 0023400213 scopus 로고
    • The optimal convergence rates of the p version of the finite element method
    • Babuška I., and Suri M. The optimal convergence rates of the p version of the finite element method. SIAM J. Numer. Anal. 24 (1987) 750-776
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 750-776
    • Babuška, I.1    Suri, M.2
  • 23
    • 0001287713 scopus 로고
    • 2 error estimates for Galerkin approximations to parabolic partial differential equations
    • 2 error estimates for Galerkin approximations to parabolic partial differential equations. SIAM J. Numer. Anal. 10 (1973) 723-759
    • (1973) SIAM J. Numer. Anal. , vol.10 , pp. 723-759
    • Wheeler, M.F.1
  • 24
    • 0002329650 scopus 로고
    • The approximation of the pressure by a mixed method in the simulation of miscible displacement
    • Douglas Jr. J., Ewing R.E., and Wheeler M.F. The approximation of the pressure by a mixed method in the simulation of miscible displacement. RAIRO Anal. Numer. 17 (1983) 17-33
    • (1983) RAIRO Anal. Numer. , vol.17 , pp. 17-33
    • Douglas Jr., J.1    Ewing, R.E.2    Wheeler, M.F.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.