ON FINITE ELEMENT METHODS FOR THE EULER-POISSON-DARBOUX EQUATION.
Genis, Anatoly M.
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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.