Numerical solution of Hamilton–Jacobi–Bellman equations by an exponentially fitted finite volume method

References

• Angermann , L and Wang , S . 2003 . Three-dimensional exponentially fitted conforming tetrahedral finite elements for the semiconductor continuity equations . Applied Numerical Mathematics , 46 : 19 – 43 .
   Google Scholar
• Bardi , M and Capuzzo-Dolcetta , I . 1997 . Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations , Boston–Basel–Berlin : Birkhäuser .
   Google Scholar
• Bardi , M , Falcone , M and Soravia , P . 1999 . “ Numerical methods for pursuit-evasion games via viscosity solutions ” . In Stochastic and Differential Games: Theory and Numerical Methods , Edited by: Bardi , M , Parthasarathy , T and Raghavan , TES . 105 – 175 . Boston : Birkhäuser .
   Google Scholar
• Crandall , MG and Lions , PL . 1983 . Three-dimensional exponentially fitted conforming tetrahedral finite elements for the semiconductor continuity equations . Applied Numerical Mathematics , 277 ( 1 ) : 1 – 42 .
   Google Scholar
• Crandall , MG , Evans , LC and Lions , PL . 1984 . Three-dimensional exponentially fitted conforming tetrahedral finite elements for the semiconductor continuity equations . Applied Numerical Mathematics , 282 ( 2 ) : 487 – 502 .
   Google Scholar
• Crandall , MG and Lions , PL . 1984 . Three-dimensional exponentially fitted conforming tetrahedral finite elements for the semiconductor continuity equations . Applied Numerical Mathematics , 43 : 1 – 19 .
   Google Scholar
• Crandall , MG , Ishii , H and Lions , PL . 1992 . Three-dimensional exponentially fitted conforming tetrahedral finite elements for the semiconductor continuity equations . Applied Numerical Mathematics , 27 : 1 – 67 .
   Google Scholar
• Delaunay , BN . 1934 . Three-dimensional exponentially fitted conforming tetrahedral finite elements for the semiconductor continuity equations . Applied Numerical Mathematics , 7 : 793 – 800 .
   Google Scholar
• Dirichlet , GL . 1850 . Three-dimensional exponentially fitted conforming tetrahedral finite elements for the semiconductor continuity equations . Applied Numerical Mathematics , 40 ( 3 ) : 209 – 227 .
   Google Scholar
• Falcone , M . Numerical solution of dynamic programming equations , Appendix in 2
   Google Scholar
• Falcone , M and Giorgo , T . 1999 . “ An approximation scheme for evolutive Hamilton-Jacobi equations ” . In Stochastic Analysis, Control, Optimization and Applications , Edited by: McEneaney , WM , George Y , G and Zhang , Q . 289 – 303 . Boston, MA : Birkhaüser Boston .
   Google Scholar
• Hird , LD , Siew , PF and Wang , S . 1999 . Three-dimensional exponentially fitted conforming tetrahedral finite elements for the semiconductor continuity equations . Applied Numerical Mathematics , 41 ( Part 1 ) : 129 – 152 .
   Google Scholar
• Huang , C-S , Wang , S and Teo , KL . 2000 . Three-dimensional exponentially fitted conforming tetrahedral finite elements for the semiconductor continuity equations . Applied Numerical Mathematics , 40 : 279 – 293 .
   Google Scholar
• Huang , C-S , Wang , S and Teo , KL . 2004 . Three-dimensional exponentially fitted conforming tetrahedral finite elements for the semiconductor continuity equations . Applied Numerical Mathematics , 166 : 153 – 166 .
   Google Scholar
• Jennings , LS , Fisher , ME , Teo , KL and Goh , CJ . MISER3 Optimal Control Software Version 3: Theory and User Manual Centre for Applied Dynamics and Optimization, The University of Western Australia. http://www.cado.uwa.edu.au/miser/manual.html
   Google Scholar
• Kushner , HJ and Dupuis , PG . 1992 . Numerical Methods for Stochastic Control Problems in Continuous Time , New York : Springer-Verlag .
   Google Scholar
• Lions , PL . 1982 . Generalised solutions of Hamilton-Jacobi equations, Research Notes in Mathematics , Vol. 69 , Boston, MA : Pitman, Advanced Publishing Program .
   Google Scholar
• Miller , JJH and Wang , S . 1991 . Three-dimensional exponentially fitted conforming tetrahedral finite elements for the semiconductor continuity equations . Applied Numerical Mathematics , 25 ( 4 ) : 441 – 463 .
   Google Scholar
• Miller , JJH and Wang , S . 1994 . Three-dimensional exponentially fitted conforming tetrahedral finite elements for the semiconductor continuity equations . Applied Numerical Mathematics , 14 : 257 – 276 .
   Google Scholar
• Miller , JJH and Wang , S . 1994 . Three-dimensional exponentially fitted conforming tetrahedral finite elements for the semiconductor continuity equations . Applied Numerical Mathematics , 115 ( 1 ) : 56 – 64 .
   Google Scholar
• Sonneveld , P . 1989 . Three-dimensional exponentially fitted conforming tetrahedral finite elements for the semiconductor continuity equations . Applied Numerical Mathematics , 10 : 36 – 52 .
   Google Scholar
• van der Vorst , HA . 1992 . Three-dimensional exponentially fitted conforming tetrahedral finite elements for the semiconductor continuity equations . Applied Numerical Mathematics , 13 : 631 – 644 .
   Google Scholar
• Varga , RS . 1962 . Matrix Iterative Analysis , Englewood Cliffs, NJ : Prentice-Hall .
   Google Scholar
• Wang , S . 1997 . Three-dimensional exponentially fitted conforming tetrahedral finite elements for the semiconductor continuity equations . Applied Numerical Mathematics , 134 : 253 – 260 .
   Google Scholar
• Wang , S , Gao , F and Teo , KL . 2000 . Three-dimensional exponentially fitted conforming tetrahedral finite elements for the semiconductor continuity equations . Applied Numerical Mathematics , 17 : 167 – 178 .
   Google Scholar
• Wang , S , Jennings , LS and Teo , KL . 2003 . Three-dimensional exponentially fitted conforming tetrahedral finite elements for the semiconductor continuity equations . Applied Numerical Mathematics , 27 : 177 – 192 .
   Google Scholar
• Wang , S and Li , ZC . 2003 . Three-dimensional exponentially fitted conforming tetrahedral finite elements for the semiconductor continuity equations . Applied Numerical Mathematics , 72 ( 244 ) : 1689 – 1709 .
   Google Scholar
• Wang , S and Angermann , L . 2003 . Three-dimensional exponentially fitted conforming tetrahedral finite elements for the semiconductor continuity equations . Applied Numerical Mathematics , 3 ( 3 ) : 493 – 512 .
   Google Scholar
• Zhou , JL , Tits , AL and Lawrence , CT . 1997 . User's guide for FFSQP version 3.7: A Fortran Code for solving constrained optimization problems, generating iterates satisfying all inequality and linear constraints Technical Report TR92-107-r2, System Research Center, University of Maryland, USA
   Google Scholar