A posteriori error estimate for finite volume approximations of nonlinear heat equations

In this contribution we derive a posteriori error estimate for finite volume approximations of nonlinear convection diffusion equations in the L∞(L^1)-norm. The problem is discretized implicitly in time by the method of characteristics, and in space by piecewise constant finite volume methods. The analysis is based on a reformulation for finite volume methods. The derived a posteriori error estimates are based on the Kruzkov technique. The idea exists of a reformulation into finite volume methods, such that the estimates, that are known in the context of the finite element methods, can be reused. Our error estimates have the correct convergence order and recover the standard a posteriori error estimates known for parabolic equations.