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Parallel Galerkin domain decomposition procedures for wave equation. (English) Zbl 1184.65092
The authors extend parallel Galerkin domain decomposition procedures for the wave equation on a general domain. Two approximation schemes are established. They use implicit Galerkin procedures in the sub-domains, called integral mean parallel domain decomposition scheme, and explicit flux calculations on the inter-boundaries of the sub-domains, called extrapolation integral mean parallel domain decomposition scheme. $L^2$ error estimates are derived for analyzing the convergence of these schemes. Results of some numerical experiments are presented.

65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
65M55Multigrid methods; domain decomposition (IVP of PDE)
65M15Error bounds (IVP of PDE)
35L05Wave equation (hyperbolic PDE)
65Y05Parallel computation (numerical methods)
65M12Stability and convergence of numerical methods (IVP of PDE)
Full Text: DOI
[1] Dupont, T. F.: L2-estimates for Galerkin methods for second-order hyperbolic equations, SIAM J. Numer. anal. 10, 880-889 (1973) · Zbl 0239.65087 · doi:10.1137/0710073
[2] Baker, G. A.: Error estimates for finite element methods for second-order hyperbolic equations, SIAM J. Numer. anal. 13, 564-576 (1976) · Zbl 0345.65059 · doi:10.1137/0713048
[3] Geveci, T.: On the application of mixed finite methods to the wave equation, RAIRO modél. Math. anal. Numér. 22, 243-250 (1988) · Zbl 0646.65083
[4] Cowsar, L. C.; Dupont, T. F.; Wheeler, M. F.: A-priori estimates for mixed finite element methods for the wave equations, Comput. methods appl. Mech. eng. 82, 205-222 (1990) · Zbl 0724.65087
[5] Baker, G. A.; Dougalis, V. A.; Serbin, S. M.: High order accurate two-step approximations for hyperbolic equations, RAIRO modél. Math. anal. Numér. 13, 201-226 (1979) · Zbl 0411.65057
[6] Safjan, A.; Oden, J. T.: High-order Taylor--Galerkin and adaptive h-p methods for second-order hyperbolic systems: applications to elastodynamics, Comput. methods appl. Mech. eng. 103, 187-230 (1993) · Zbl 0767.73077
[7] French, D. A.; Peterson, T. E.: A continuous space-time finite element method for the wave equation, Math. comput. 66, 491-506 (1996) · Zbl 0846.65048
[8] Bramble, J. H.; Pasciak, J. E.; Xu, J.: Convergence estimates for product iterative methods with application to domain decomposition, Math. comput. 57, 1-21 (1991) · Zbl 0754.65085 · doi:10.2307/2938660
[9] Cai, X. C.: Multiplicative Schwarz methods for parabolic problem, SIAM J. Sci. comput. 15, 587-603 (1994) · Zbl 0803.65096
[10] Dawson, C. N.; Dupont, T. F.: Explicit/implicit conservative Galerkin domain decomposition procedures for parabolic problems, Math. comput. 58, 21-35 (1992) · Zbl 0746.65072 · doi:10.2307/2153018
[11] Xu, J.: Iterative methods by space decomposition and subspace correction: A unifying approach, SIAM rev. 34, 581-613 (1992) · Zbl 0788.65037 · doi:10.1137/1034116
[12] Rui, H.; Yang, D. P.: Schwarz type domain decomposition algorithms for parabolic equations and error estimates, Acta. math. Appl. sinica 14, 300-313 (1998) · Zbl 0934.35059 · doi:10.1007/BF02677411
[13] Tai, X. C.: A space decomposition method for parabolic equations, Numer methods partial differential equations 14, 24-46 (1998) · Zbl 0891.65104 · doi:10.1002/(SICI)1098-2426(199801)14:1<27::AID-NUM2>3.0.CO;2-N
[14] Wheeler, M. F.: A priori L2 error estimates for Galerkin approximations to parabolic partial differential equations, SIAM J. Numer. anal. 10, 723-759 (1973) · Zbl 0232.35060 · doi:10.1137/0710062
[15] Bramble, J. H.; Schatz, A. H.: Higher order local accuracy by averaging in the finite element method, Math. comput. 31, 94-111 (1977) · Zbl 0353.65064 · doi:10.2307/2005782
[16] Ma, Keying; Sun, Tongjun; Yang, Danping: Galerkin domain decomposition procedures for parabolic equation of general form on general domain, Numer methods partial differential equations 25, No. 5, 1167-1194 (2009) · Zbl 1173.65061 · doi:10.1002/num.20394
[17] Keying Ma, Tongjun Sun, Galerkin domain decomposition procedures for parabolic equations on rectangular domain, Int. J. Numer. Meth. Fluids, published online for early view. doi:10.1002/fld.2028 · Zbl 1187.65109
[18] Dupont, T. F.: Non-iterative domain decomposition for second order hyperbolic problems, Proc. sixth int. Conf. on domain decomposition meths (1994) · Zbl 0804.65097
[19] Bamberger, A.; Glowinski, R.; Tran, Q. H.: A domain decompostition method for the acoustic wave equation with discontinuous coefficients and grid change, SIAM J. Numer. anal. 34, 603-639 (1997) · Zbl 0877.35066 · doi:10.1137/S0036142994261518
[20] Dean, E. J.; Glowinski, R.: Domain decompostition methods for mixed finite element approximations of wave problems, Comput. math. Appl. 38, 207-214 (1999) · Zbl 0949.65100 · doi:10.1016/S0898-1221(99)00251-5
[21] Ciarlet, P. G.: The finite element method for elliptic problems, (1978) · Zbl 0383.65058
[22] Nitsche, J.: L\infty-error analysis for finite elements, The mathematics of finite elements and applications III, 173-186 (1979) · Zbl 0449.65078
[23] Schatz, A. H.; Wahlbin, L. B.: Maximun norm estimates in the finite element method on plane polygonal domains, I, Math. comput. 32, 73-109 (1978) · Zbl 0382.65058 · doi:10.2307/2006259
[24] Schatz, A. H.; Wahlbin, L. B.: Maximun norm estimates in the finite element method on plane polygonal domains, II, Math. comput. 33, 485-492 (1979) · Zbl 0417.65053 · doi:10.2307/2006291
[25] Brenner, S. C.; Scott, L. R.: The mathematical theory of finite element methods, Texts in applied mathematics 15 (1996) · Zbl 0804.65101