메뉴 건너뛰기




Volumn 33, Issue 2, 2011, Pages 893-922

Superconvergent functional estimates from summation-by-parts finite-difference discretizations

Author keywords

Dual consistency; Finite difference schemes; Functional estimates; Simultaneous approximation terms; Summation byparts operators; Superconvergence

Indexed keywords

FINITE DIFFERENCE METHOD; FLUID MECHANICS; NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS;

EID: 79957605252     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/100790987     Document Type: Article
Times cited : (75)

References (35)
  • 2
    • 0041482082 scopus 로고
    • Total flux estimates for a finite-element approximation of elliptic equations
    • J. W. BARRETT AND C. M. ELLIOTT, Total flux estimates for a finite-element approximation of elliptic equations, IMA J. Numer. Anal., 7 (1987), pp. 129-148.
    • (1987) IMA J. Numer. Anal. , vol.7 , pp. 129-148
    • Barrett, J.W.1    Elliott, C.M.2
  • 3
    • 84875280850 scopus 로고
    • Higher order local accuracy by averaging in the finite element method
    • J. H. BRAMBLE AND A. H. SCHATZ, Higher order local accuracy by averaging in the finite element method, Math. Comp., 31 (1977), pp. 94-111.
    • (1977) Math. Comp. , vol.31 , pp. 94-111
    • Bramble, J.H.1    Schatz, A.H.2
  • 4
    • 0001473098 scopus 로고
    • Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes
    • DOI 10.1006/jcph.1994.1057
    • M. H. CARPENTER, D. GOTTLIEB, AND S. ABARBANEL, Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to highorder compact schemes, J. Comput. Phys., 111 (1994), pp. 220-236. (Pubitemid 124013392)
    • (1994) Journal of Computational Physics , vol.111 , Issue.2 , pp. 220-236
    • Carpenter, M.H.1
  • 5
    • 0000926967 scopus 로고    scopus 로고
    • A stable and conservative interface treatment of arbitrary spatial accuracy
    • M. H. CARPENTER, J. NORDSTRÖM, AND D. GOTTLIEB, A stable and conservative interface treatment of arbitrary spatial accuracy, J. Comput. Phys., 148 (1999), pp. 341-365.
    • (1999) J. Comput. Phys. , vol.148 , pp. 341-365
    • Carpenter, M.H.1    Nordström, J.2    Gottlieb, D.3
  • 6
    • 77956187008 scopus 로고    scopus 로고
    • Revisiting and extending interface penalties for multi-domain summation-by-parts operators
    • M. H. CARPENTER, J. NORDSTRÖM, AND D. GOTTLIEB, Revisiting and extending interface penalties for multi-domain summation-by-parts operators, J. Sci. Comput., 45 (2010), pp. 118-150.
    • (2010) J. Sci. Comput. , vol.45 , pp. 118-150
    • Carpenter, M.H.1    Nordström, J.2    Gottlieb, D.3
  • 7
    • 0000319158 scopus 로고
    • Collocation at Gaussian points
    • C. de BOOR AND B. SWARTZ, Collocation at Gaussian points, SIAM J. Numer. Anal., 10 (1973), pp. 582-606.
    • (1973) SIAM J. Numer. Anal. , vol.10 , pp. 582-606
    • De Boor, C.1    Swartz, B.2
  • 8
    • 34250840018 scopus 로고    scopus 로고
    • Optimized high-order derivative and dissipation operators satisfying summation by parts, and applications in three-dimensional multi-block evolutions
    • DOI 10.1007/s10915-006-9123-7
    • P. DIENER, E. N. DORBAND, E. SCHNETTER, AND M. TIGLIO, Optimized high-order derivative and dissipation operators satisfying summation by parts, and applications in threedimensional multi-block evolutions, J. Sci. Comput., 32 (2007), pp. 109-145. (Pubitemid 46981137)
    • (2007) Journal of Scientific Computing , vol.32 , Issue.1 , pp. 109-145
    • Diener, P.1    Dorband, E.N.2    Schnetter, E.3    Tiglio, M.4
  • 9
    • 84968494170 scopus 로고
    • A new method of imposing boundary conditions in pseudospectral approximations of hyperbolic equations
    • D. FUNARO AND D. GOTTLIEB, A new method of imposing boundary conditions in pseudospectral approximations of hyperbolic equations, Math. Comp., 51 (1988), pp. 599-613.
    • (1988) Math. Comp. , vol.51 , pp. 599-613
    • Funaro, D.1    Gottlieb, D.2
  • 10
    • 0000983134 scopus 로고
    • The convergence rate for difference approximations to general mixed initial boundary value problems
    • B. GUSTAFSSON, The convergence rate for difference approximations to general mixed initial boundary value problems, SIAM J. Numer. Anal., 18 (1981), pp. 179-190.
    • (1981) SIAM J. Numer. Anal. , vol.18 , pp. 179-190
    • Gustafsson, B.1
  • 12
    • 55749106415 scopus 로고    scopus 로고
    • A parallel Newton-Krylov solver for the Euler equations discretized using simultaneous approximation terms
    • J. E. HICKEN AND D. W. ZINGG, A parallel Newton-Krylov solver for the Euler equations discretized using simultaneous approximation terms, AIAA J., 46 (2008), pp. 2773-2786.
    • (2008) AIAA J. , vol.46 , pp. 2773-2786
    • Hicken, J.E.1    Zingg, D.W.2
  • 14
    • 73249133123 scopus 로고    scopus 로고
    • High-order narrow stencil finite-difference approximations of second-order derivatives involving variable coefficients
    • R. KAMAKOTI AND C. PANTANO, High-order narrow stencil finite-difference approximations of second-order derivatives involving variable coefficients, SIAM J. Sci. Comput., 31 (2009), pp. 4222-4243.
    • (2009) SIAM J. Sci. Comput. , vol.31 , pp. 4222-4243
    • Kamakoti, R.1    Pantano, C.2
  • 15
    • 0003279949 scopus 로고
    • Finite element and finite difference methods for hyperbolic partial differential equations
    • C. de Boor, ed., Academic Press, New York
    • H.-O. KREISS AND G. SCHERER, Finite element and finite difference methods for hyperbolic partial differential equations, in Mathematical Aspects of Finite Elements in Partial Differential Equations, C. de Boor, ed., Academic Press, New York, 1974, pp. 195-212.
    • (1974) Mathematical Aspects of Finite Elements in Partial Differential Equations , pp. 195-212
    • Kreiss, H.-O.1    Scherer, G.2
  • 17
    • 29044433670 scopus 로고    scopus 로고
    • Multi-block simulations in general relativity: High-order discretizations, numerical stability and applications
    • DOI 10.1088/0264-9381/22/24/006, PII S0264938105036944
    • L. LEHNER, O. REULA, AND M. TIGLIO, Multi-block simulations in general relativity: Highorder discretizations, numerical stability and applications, Classical Quantum Gravity, 22 (2005), pp. 5283-5321. (Pubitemid 41787647)
    • (2005) Classical and Quantum Gravity , vol.22 , Issue.24 , pp. 5283-5321
    • Lehner, L.1    Reula, O.2    Tiglio, M.3
  • 20
    • 0347090590 scopus 로고    scopus 로고
    • Boundary procedures for summation-by-parts operators
    • K. MATTSSON, Boundary procedures for summation-by-parts operators, J. Sci. Comput., 18 (2003), pp. 133-153.
    • (2003) J. Sci. Comput. , vol.18 , pp. 133-153
    • Mattsson, K.1
  • 21
    • 4544273333 scopus 로고    scopus 로고
    • Summation by parts operators for finite difference approximations of second derivatives
    • DOI 10.1016/j.jcp.2004.03.001, PII S0021999104000932
    • K. MATTSSON AND J. NORDSTRÖM, Summation by parts operators for finite difference approximations of second derivatives, J. Comput. Phys., 199 (2004), pp. 503-540. (Pubitemid 39216323)
    • (2004) Journal of Computational Physics , vol.199 , Issue.2 , pp. 503-540
    • Mattsson, K.1    Nordstrom, J.2
  • 22
    • 4544230753 scopus 로고    scopus 로고
    • Stable and accurate artificial dissipation
    • K. MATTSSON, M. SVÄRD, AND J. NORDSTRÖM, Stable and accurate artificial dissipation, J. Sci. Comput., 21 (2004), pp. 57-79.
    • (2004) J. Sci. Comput. , vol.21 , pp. 57-79
    • Mattsson, K.1    Svärd, M.2    Nordström, J.3
  • 23
    • 38049046095 scopus 로고    scopus 로고
    • Stable and accurate schemes for the compressible Navier-Stokes equations
    • K. MATTSSON, M. SVÄRD, AND M. SHOEYBI, Stable and accurate schemes for the compressible Navier-Stokes equations, J. Comput. Phys., 227 (2008), pp. 2293-2316.
    • (2008) J. Comput. Phys. , vol.227 , pp. 2293-2316
    • Mattsson, K.1    Svärd, M.2    Shoeybi, M.3
  • 24
    • 0035841069 scopus 로고    scopus 로고
    • High-order finite difference methods, multidimensional linear problems, and curvilinear coordinates
    • DOI 10.1006/jcph.2001.6864
    • J. NORDSTRÖM AND M. H. CARPENTER, High-order finite difference methods, multidimensional linear problems, and curvilinear coordinates, J. Comput. Phys., 173 (2001), pp. 149-174. (Pubitemid 33098511)
    • (2001) Journal of Computational Physics , vol.173 , Issue.1 , pp. 149-174
    • Nordstrom, J.1    Carpenter, M.H.2
  • 25
    • 70350018301 scopus 로고    scopus 로고
    • A stable and conservative high order multi-block method for the compressible Navier-Stokes equations
    • J. NORDSTRÖM, J. GONG, E. VAN DER WEIDE, AND M. SVÄRD, A stable and conservative high order multi-block method for the compressible Navier-Stokes equations, J. Comput. Phys., 228 (2009), pp. 9020-9035.
    • (2009) J. Comput. Phys. , vol.228 , pp. 9020-9035
    • Nordström, J.1    Gong, J.2    Van Der Weide, E.3    Svärd, M.4
  • 26
    • 78649808521 scopus 로고    scopus 로고
    • A parallel Newton-Krylov-Schur flow solver for the Navier-Stokes equations using the SBP-SAT approach
    • Orlando, FL, AIAA-2010-0116
    • M. OSUSKY, J. E. HICKEN, AND D. W. ZINGG, A parallel Newton-Krylov-Schur flow solver for the Navier-Stokes equations using the SBP-SAT approach, in 48th AIAA Aerospace Sciences Meeting, Orlando, FL, 2010, AIAA-2010-0116.
    • (2010) 48th AIAA Aerospace Sciences Meeting
    • Osusky, M.1    Hicken, J.E.2    Zingg, D.W.3
  • 27
    • 69249146102 scopus 로고    scopus 로고
    • Orbiting binary black hole evolutions with a multipatch high order finite-difference approach
    • E. PAZOS, M. TIGLIO, M. D. DUEZ, L. E. KIDDER, AND S. A. TEUKOLSKY, Orbiting binary black hole evolutions with a multipatch high order finite-difference approach, Phys. Rev. D, 80 (2009), 024027.
    • (2009) Phys. Rev. D , vol.80 , pp. 024027
    • Pazos, E.1    Tiglio, M.2    Duez, M.D.3    Kidder, L.E.4    Teukolsky, S.A.5
  • 28
    • 0034206154 scopus 로고    scopus 로고
    • Adjoint recovery of superconvergent functionals from PDE approximations
    • N. A. PIERCE AND M. B. GILES, Adjoint recovery of superconvergent functionals from PDE approximations, SIAM Rev., 42 (2000), pp. 247-264.
    • (2000) SIAM Rev. , vol.42 , pp. 247-264
    • Pierce, N.A.1    Giles, M.B.2
  • 29
    • 0018984826 scopus 로고
    • Implicit finite-difference simulations of three-dimensional compressible flow
    • T. H. PULLIAM AND J. L. STEGER, Implicit finite-difference simulations of three-dimensional compressible flow, AIAA J., 18 (1980), pp. 159-167.
    • (1980) AIAA J. , vol.18 , pp. 159-167
    • Pulliam, T.H.1    Steger, J.L.2
  • 30
    • 67349262500 scopus 로고    scopus 로고
    • On problems associated with grid convergence of functionals
    • M. D. SALAS AND H. L. ATKINS, On problems associated with grid convergence of functionals, Comput. & Fluids, 38 (2009), pp. 1445-1454.
    • (2009) Comput. & Fluids , vol.38 , pp. 1445-1454
    • Salas, M.D.1    Atkins, H.L.2
  • 31
    • 0002449864 scopus 로고
    • Summation by Parts for Finite Difference Approximations for d/dx
    • DOI 10.1006/jcph.1994.1005
    • B. STRAND, Summation by parts for finite difference approximations for d/dx, J. Comput. Phys., 110 (1994), pp. 47-67. (Pubitemid 124013344)
    • (1994) Journal of Computational Physics , vol.110 , Issue.1 , pp. 47-67
    • Strand, B.1
  • 32
    • 0345872005 scopus 로고    scopus 로고
    • On coordinate transformations for summation-by-parts operators
    • M. SVÄRD, On coordinate transformations for summation-by-parts operators, J. Sci. Comput., 20 (2004), pp. 29-42.
    • (2004) J. Sci. Comput. , vol.20 , pp. 29-42
    • Svärd, M.1
  • 33
    • 33748544239 scopus 로고    scopus 로고
    • On the order of accuracy for difference approximations of initial-boundary value problems
    • DOI 10.1016/j.jcp.2006.02.014, PII S0021999106000878
    • M. SVÄRD AND J. NORDSTRÖM, On the order of accuracy for difference approximations of initial-boundary value problems, J. Comput. Phys., 218 (2006), pp. 333-352. (Pubitemid 44364192)
    • (2006) Journal of Computational Physics , vol.218 , Issue.1 , pp. 333-352
    • Svard, M.1    Nordstrom, J.2
  • 34
    • 0018529022 scopus 로고
    • Geometric conservation law and its application to flow computations on moving grids
    • P. D. THOMAS AND C. K. LOMBARD, Geometric conservation law and its application to flow computations on moving grids, AIAA J., 17 (1979), pp. 1030-1037. (Pubitemid 10412273)
    • (1979) AIAA Journal , vol.17 , Issue.10 , pp. 1030-1037
    • Thomas, P.D.1
  • 35
    • 0016115895 scopus 로고
    • Convergence estimates for Galerkin methods for variable coefficient initial value problems
    • V. THOMÉE AND B. WENDROFF, Convergence estimates for Galerkin methods for variable coefficient initial value problems, SIAM J. Numer. Anal., 11 (1974), pp. 1059-1068.
    • (1974) SIAM J. Numer. Anal. , vol.11 , pp. 1059-1068
    • Thomée, V.1    Wendroff, B.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.