A Galerkin Method for Elliptic-Hyperbolic Type Equations

A certain Galerkin-type method is proposed for the numerical solution of a class of second order linear mixed-type partial differential equations. Convergence of such an approximation is proved in the whole region of definition. Error estimates are derived in a natural norm assuming smooth solutions.Numerical experiments are conducted using bicubic splines. The obtained results show that solutions are approximated equally well in both elliptic and hyperbolic regions.