On the Physical Interpretation of the Sobolev Norm in Error Estimation

摘要

Error estimates for the moment method have been obtained in terms of Sobolev norms of the current solution. Motivated by the historical origins of Sobolev spaces as energy spaces, we show that the Sobolev norm used in these estimates is related to the forward scattering amplitude, for the case of 2D scattering from a PEC circular cylinder and for 3D scattering from a PEC sphere. These results provide a physical meaning for solution error estimates in terms of the power radiated by the error in the current solution. We further show that bounds on the Sobolev norm of the current error imply a bound on the error in the computed backscattering amplitude.