Numer. Math. 44, 371-391 (1984) Numerische MathemalJk 9 Springer-Verlag 1984 Approximation of Tricomi Problem with Neumann Boundary Condition M. Vanninathan and G.D. Veerappa Gowda T.I.F.R. Centre, P.O. Box 1234, Bangalore 560012, India Summary. The Tricomi problem with Neumann boundary condition is reduced to a degenerate problem in the elliptic region with a non-local boundary condition and to a Cauchy problem in the hyperbolic region. A variational formulation is given to the elliptic problem and a finite element approximation is studied. Also some regularity results in weighted Sobolev spaces are discussed. Subject Classification: AMS(MOS): 65N30, CR: G 1.8. 1. Introduction It is well-known that transonic flows of gases are modelled by Tricomi equa- tion. Bers [2]: Tu - YUxx + uyy = 0. (1) In this paper, we consider the above equation in a domain G in the plane R2. We pose I2=Gn{y>O}. (2) We assume the boundary of G consists of three parts Z, F and F~ where E lies in the upper half plane, F and F 1 are the characteristics through (0,0) and (1,0) respectively described by F: x =2(_y)3/2, _(88 <y<0, r~: x+](-y) 3/2 = i, -( 88 <y<0. ~,~/e suppose further that t2 is convex E coincides with the linbs x = 0 and x = 1 for small enough y > 0. (3) (4)