The Time Continuous Space Discontinuous Fully Element Finite Method For First Order Hyperbolic Equation

The study of the first order hyperbolic equation and its equation set has always been a hot topic for many scholars.In this paper,a new idea is adopt to study the first order hyperbolic equation,that is,the time continuous and space discontinuous element finite method.On the basis of energy method and tensor integral solution,by means of the idea of test function projection,M-type and Radau-type were constructed by unit orthogonal analysis,It is simply proved that the first order hyperbolic equation is time continuous,space discontinuous element finite method of the full order integral error estimates.And the use of partial differential projection proved the super convergence over the right node.The results of numerical experiment confirmed the theory,all the results show that the first-order hyperbolic a direction with the equation of continuous for another direction with discontinuous is feasible,and be a double super space-time convergence.