Improved error estimates for mixed finite element for nonlinear hyperbolic equations: The continuous-time case (Q2748456)

The authors investigate the convergence behavior of a mixed finite element semi-discretization applied to nonlinear hyperbolic equations in two spatial variables. For semi-discretization Raviart-Thomas elements of lowest order are used. Basic estimates known from literature [e.g. \textit{Y. Kwon} and \textit{F. A. Milner}, SIAM J. Numer. Anal. 25, No. 1, 46-53 (1988; Zbl 0643.65057)] completed with detailed further estimates prepare a new superconvergence bound as main result which is of type NEWLINE\[NEWLINE \|(u-U)_t\|_{L^\infty(L^2)}+ \|u-U\|_{L^\infty(L^2)}+\|z-Z\|_{L^\infty(L^2)} \leq C(u) h^rNEWLINE\]NEWLINE for \(1\leq r\leq k+1\), \(k\geq 0\).