SIAM Journal on Scientific Computing
We deal primarily with the derivation of various convergence estimates for some semidiscrete and fully discrete procedures which might be used in the approximation of exact solutions of initial-boundary value problems with homogeneous Dirichlet boundary conditions for the Euler-Poisson-Darboux equation. Although the equation is of hyperbolic type, the results are somewhat analogous to those known for parabolic equations, due to the presence of a limited 'smoothing' property. This paper contain L//2 estimates, maximum norm estimates, negative norm estimates, interior estimates of difference quotients and superconvergence estimates of the error.
Genis, A. M. (1984). ON FINITE ELEMENT METHODS FOR THE EULER-POISSON-DARBOUX EQUATION. SIAM Journal on Numerical Analysis, 21(6), 1080-1106.