GALERKIN ALTERNATING-DIRECTION METHODS FOR A KIND OF THREE-DIMENSIONAL QUASI-LINEAR HYPERBOLIC EQUATIONS
一类三维拟线性双曲型方程交替方向有限元法

A kind of second-order three-dimensional quasi-linear hyperbolic equation is firstly transformed into a system of first-order equations, then the Galerkin alternating-direction procedure for the system is derived. The optimal order estimates in H1 norm and L2 norm of the procedure are obtained respectively by using the theory and techniques of priori estimate of differential equations. The numerical experiment is also given to support the theoretical analysis. Comparison the results of numerical example with the theoretical analysis shows they are uniform.