A finite element method for the nonlinear Tricomi problem

Summary We consider a finite element procedure for numerical solution of the nonlinear problem:L[u]=yu_xx+u_yy+r(x,y)u=f(x, y, u) in a simply connected regionG in thex-y plane. The boundary ofG consists of ₀, ₁, and ₂ and we impose the boundary condition. ₀ is assumed to be a piecewises smooth curve lying in the half-planey>0 with endpointsA(–1, 0) andB(0, 0). ₁ and ₂ are characteristics of the operatorL issued fromA andB which intersect at the pointC(–1/2,y_c). An error analysis of the method is also given.