Time Finite Element Method Solving Dynamics And Heat Transfer Problems

Time-dependent problems play an important role in many engineering aspects, such as elastic dynamics, heat conduction etc. Study on time-dependent problems is dramatically significant theoretically and practically.A method of setting up numerical models is presented in this paper by applying adaptive space-discretization. A series of recursive formulas are deduced through a conventional weighted residual technique in time domain. Convenience, practicality and high precision of this method are exhibited by numerical examples.Main work of this paper includes1, Applying a conventional weighted residual technique, to a series of ordinary differential equation through the spatial discretization, utilizing the discretization of Lagrange interpolation and the technique of finite element method, deduced the recurrence form of the time finite element method above the first-order and second-order system.2, Based on the theories mentioned above, deduced the time finite element method about the solution of the one-dimension dynamics problem and do the research of stability.3, Based on the same theories, deduced the time finite element method about the solution of the parabolic and hyperbolic heat transfer problems.4, A couple of numerical examples on dynamic problems and heat transfer problems are given and the numerical results show that this method can be used to solve the ordinary differential equations with spatial discretization, numerical solutions show its reliable precision and great applications in engineering.