Galerkin alternating-direction methods for a kind of nonlinear hyperbolic equations on nonrectangular regions

Patch approximation and an approximation to the Jacobian of the isoparametric map are applied to discuss a three-level and a four-level Galerkin alternating-direction procedures for a kind of nonlinear hyperbolic equation which is given on a nonrectangular, curved region. With these procedures, multi-dimensional problems can be solved as a series of one-dimensional problems. And the L2 norm error estimates are derived.