Improved Error Estimates for Mixed Finite Element for Nonlinear Hyperbolic Equations: The Continuous-Time Case

Abstract

Improved $L_2$-error estimates are computed for mixed finite element methods for second order nonlinear hyperbolic equations. Results are given for the continuous-time case. The convergence of the values for both the scalar function and the flux is demonstrated. The technique used here covers the lowest-order Raviart-Thomas spaces, as well as the higher-order spaces. A second paper will present the analysis of a fully discrete scheme.