[1] Allen E J, Novosel S J, Zhang Z. Finite element and difference approximation of some linear stochastic partical differential equations, Stoch. stoch. Rep. 1998, 64(1-2):117-142.[2] Babuška I, Tempone R, Zouraris G E. Galerkin finite element approximations of stochastic elliptic partial differential equations, SIAM J. Numer. Anal. 2004, 42(2):800-825.[3] Brzézniak Z, Maslowski B, Seidler J. Stochastic nonlinear beam equations, Probab. Theory Relat. Field. 2005, 132:119-149.[4] Cao Y Z, Yang H T, Yin L. Finite element methods for semilinear elliptic stochastic partial differential equations, Numer. Math. 2007, 106:181-198.[5] Chow P L, Menaldi J L. Stochastic PDE for nonlinear Vibration of elastic panels, Diff. Int. Eqns. 1999, 12(3):419-434.[6] Debussche A, Printems J.Weak order for the discretization of the stochastic heat equation, Math. Comput. 2009, 78:845-863.[7] Dong H J, Krylov N V. On the rate of convergence of finite-difference approximations for degenerate linear parabolic equations with C1 and C2 coefficients, Electron. J. Diff. Eqns. 2005, 102:1-25.[8] Du Q, Zhang T Y. Numerical approximation of some linear stochastic partial differential equations driven by special additive noise, SIAM J. Numer. Anal. 2002, 4:1421-1445.[9] Galal O L, El-Tawil M A, Mahmoud A A. Stochastic beam equations under random dynamic loads, Inter. J. Solid. Struct. 2002, 39:1031-1040.[10] Gyöngy I, Nualart D. Implicit scheme for stochastic parabolic partial differential equations driven by space-time white noise, Potential Anal. 1997, 7(4):725-757.[11] Gyöngy I. Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by space-time white noise I, Potential Anal. 1998, 9(1):1-25.[12] Gyöngy I. Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by space-time white noise Ⅱ, Potential Anal. 1999, 11(1):1-37.[13] Gyöngy I, Krylov N. On the splitting-up method and stochastic partial differential equations, Ann. Probab. 2003, 31(2):564-991.[14] Gyöngy I, Millet A. On discretization schemes for stochastic evolution equations, Potential Anal. 2005, 23:99-134.[15] Gyöngy I, Krylov N V. An accelerated splitting-up method for parabolic equations, SIAM J. Math. Anal. 2006, 37:1070-1097.[16] Gyöngy I, Martínez T. On numerical solution of stochastic partial differential equations of elliptic type, Stochatics, 2006, 78(4):213-231.[17] Gyöngy I, Krylov N V. Accelerated finite difference schemes for stochastic parabolic partial differential equations in the whole space, SIAM J. Math. Anal. 2010, 42(5):2275-2296.[18] Gyöngy I, Krylov N V. Accelerated finite difference schemes for second order degenerate elliptic and parabolic problems in the whole space, Math. Comput. 2011, 80:1431-1458.[19] Higham D J. An algorighmic introduction to numerical simulation of stochastic differential equations, SIAM Review, 2001, 43(3):525-546.[20] Jentzen A, Kloeden P E. The numerical approximation of stochastic partical differential equations, Milan J. Math. 2009, 77:205-244.[21] Kim J U. On a stochatic plate equation, Appl. Math. Optim. 2001, 44:33-48.[22] Kloeden P, Platen E. Numerical solution of stochastic differential equations, Springer-Verlag, Berlin, 1992.[23] Kovács M, Larsson S, Lindgren F. Strong convergence of the finite element method with truncated noise for semilinear parabolic stochastic equations, Numer. Algor. 2010, 53: 309-320.[24] Martin A, Prigarin S M, Winkler G. Exact and fast numerical algorithms for the stochastic wave equation, Int. J. Comput. Math. 2003, 80(12):1535-1541.[25] Prato G D, Zabczyk J. Stochastic equations in infinite dimensions, Cambridge University press, Cambridge, UK, 1992.[26] Prévôt C, Röckner M. A concise course on stochastic differential equations, Lecture Notes in Mathmatics, Springer, Berlin, 2007.[27] Printems J. On the discretization in time of parabolic stochastic partial differential equtions, Math. Model. Numer. Anal. 2001, 35(6):1055-1078.[28] Qi R, Yang X, Zhang Y. Full-Discrete Finite Element Method for the Stochastic Elastic Equation Driven by Additive Noise, Numer. Methods Partial Differential Eq. 2013, 29: 1946-1962.[29] Lluís Quer-Sardanyons, Marta Sanz-Solé, Space semi-discretizations for a stochastic wave equation, Potential Anal. 2006, 24:303-332.[30] Walsh J B. An introduction to stochastic partial differential equations, Lecture Notes in Mathematics, 1180, Springer-verlag, Berlin, 1986, 265-439.[31] Woinowsky-Krieger S. The effect of an axial force on the vibration of hinged bars, J. Appl. Mech. 1950, 17:35-36.[32] Yan Y. Galerkin finite element methods for stochastic parabolic partial differential equations, SIAM J. Numer. Anal. 2005, 43(4):1363-1384.[33] Yoo H. Semi-discretization of stochastic partial differential equations on R1 by a finitedifference method, Math. Comput. 2000, 69:653-666.[34] Zhang T. Large deviations for stochastic nonlinear beam equations, J. Funct. Anal. 2007, 248:175-201. |