SOLVING BOUNDARY-VALUE-PROBLEMS USING HP-VERSION FINITE-ELEMENTS IN TIME

An hp-version finite element method for one-dimensional boundary value problems is presented. The method is based on a similar approach deve loped by the authors for solution of optimal control problems. The pri mary applications for the methodology include two-point- and multi-poi nt-boundary-value problems, for example, in the time domain. Results p resented for a 7-state/3-phase missile problem show that the method is very efficient for time-marching applications. Furthermore, it easily solves time-domain problems with discontinuities in the system equati ons and/or in the states, where the time at which these jumps (i.e. 'e vents') take place is determined by equations that govern the states. An example involving friction with intermittent sticking is presented to illustrate the power of the method. (C) 1998 John Wiley & Sons, Ltd .