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This article concerns a scalar multidimensional conservation law where theflux is of Panov type and may contain spatial discontinuities. We define anotion of entropy solution and prove that entropy solutions are unique. Wepropose a Godunov-type finite volume scheme and prove that the Godunovapproximations converge to an entropy solution, thus establishing existence ofentropy solutions. We also show that our numerical scheme converges at anoptimal rate of $\mathcal{O}(\sqrt{\D t}).$ To the best of our knowledge,convergence of the Godunov type methods in multi-dimension and error estimatesof the numerical scheme in one as well as in several dimensions are the firstof it's kind for conservation laws with discontinuous flux. We presentnumerical examples that illustrate the theory.

A Godunov type scheme and error estimates for multidimensional scalar conservation laws with Panov-type discontinuous flux