Toward a general solution verification method for complex PDF problem with hands off coding

The goal of this paper is to present a versatile framework for the solution verification of complex partial differential equation problems. Our goal is to produce an a posteriori error estimate with no internal knowledge of the simulation code that computes the solution. Our method decomposes into an optimization procedure that reconstruct the best consistent solution from two or three coarse grid solutions and a perturbation technique that estimate the conditioning number of the problem. Because this procedure is cumbersome and may involve hundred of uncoupled small computations, we use distributed computing to compute the a posteriori error bound.

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