References
- Aihara , S. I. and Bagchi , A. 2005 . Stochastic hyperbolic dynamics for infinite-dimensional forward rates and option pricing . Math. Finance , 15 : 27 – 47 .
- Allen , E. J. , Novosel , S. J. and Zhang , Z. 1998 . Finite element and difference approximation of some linear stochastic partial differential equations . Stoch. Stoch. Rep. , 64 : 117 – 142 .
- Björk , T. 1998 . “ Arbitrage Theory in Continuous Time ” . New York : Oxford University Press .
- Chevaugeon , N. , Hillewaert , K. , Gallez , X. , Ploumhans , P. and Remacle , J. 2007 . Optimal numerical parameterization of discontinuous Galerkin method applied to wave propagation problems . J. Comput. Phys. , 223 : 188 – 207 .
- Chioma , C. L. and Piccoli , B. 2007 . Heath–Jarrow–Morton interest rate dynamics and approximately consistent forward rate curves . Math. Finance , 17 : 427 – 447 .
- Ciarlet , P. 1978 . “ The Finite Element Method for Elliptic Problems ” . Amsterdam : North-Holland .
- Cockburn , B. and Gremaud , P. 1996 . Error estimates for finite element methods for scalar conservation laws . SIAM J. Numer. Anal. , 33 ( 2 ) : 522 – 554 .
- Cockburn , B. and Shu , C. 1989 . TVB Runge–Kutta local projection discontinuous Galerkin finite element method for conservation laws II: General framework . Math. Comput. , 52 ( 186 ) : 411 – 435 .
- Heath , D. , Jarrow , R. and Morton , A. 1992 . Bond pricing and the term structure of interest rates: A new methodology . Econometrica , 60 : 77 – 105 .
- Hughes , T. J.R. and Brooks , A. 1982 . “ Theoretical framework for Petrov–Galerkin methods with discontinuous weighting functions: Application to the streamline-upwind procedure ” . In Finite Elements in Fluids , Edited by: Gallagher , R. H. , Norrie , D. N. , Oden , J. T. and Zienkiewicz , O. C. 46 – 65 . London : Wiley .
- Marchandise , E. , Chevaugeon , N. and Remacle , J. 2008 . Spatial and spectral superconvergence of discontinuous Galerkin method for hyperbolic problems . J. Comput. Appl. Math. , 215 : 484 – 494 .
- Miller , K. and Baines , M. 2001 . Least squares moving finite elements . IMA J. Numer. Anal. , 21 : 621 – 642 .
- Musiela , M. 1993 . “ Stochastic PDEs and Term Structure Models ” . In Journee Internationales de Finance IGR-AFFI, La Boule
- Saenger , E. H. , Gold , N. and Shapiro , S. A. 2000 . Modeling the propagation of the waves using a modified finite-difference grid . Wave Motion , 31 : 77 – 92 .
- Saleh , M. M. , El-Kalla , I. L. and Ehab , M. M. 2007 . Stochastic finite element technique for stochastic one-dimension time-dependent differential equations with random coefficients . Differ. Equ. Nonlinear Mech. , 2007 : 16 Article ID 48527
- Walsh , J. B. 2006 . On numerical solutions of the stochastic wave equation . Illinois J. Math. , 50 ( 4 ) : 991 – 1018 .