Under an unproved BV-stability hypothesis, finite volume and two-stage RKDG methods with abstract limiting get a conditional L1 error estimate of order h^(1/3).
Hyperbolic systems of conservation laws , volume 20 of Oxford Lecture Series in Mathematics and its Applications
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Conditional a priori error estimates of finite volume and Runge-Kutta discontinuous Galerkin methods with abstract limiting for hyperbolic systems of conservation laws in 1D
Under an unproved BV-stability hypothesis, finite volume and two-stage RKDG methods with abstract limiting get a conditional L1 error estimate of order h^(1/3).