This paper establishes a ${\mathcal O}(h^{\frac14})$ error estimate in the $L_t^\infty(L_x^1)$-norm for the approximation of scalar conservation equations using an explicit continuous finite element technique. A general a priori error estimate based on entropy inequalities is also given in the appendix.
['Jean-Luc Guermond', 'Bojan Popov']
Error Estimates of a First-order Lagrange Finite Element Technique for Nonlinear Scalar Conservation Equations