Combination technique coefficients via error splittings

Abstract

We investigate a new way of choosing combination coefficients for the sparse grid combination technique. Previous work considered choosing coefficients such that the interpolation error of sufficiently smooth functions is minimised. We instead obtain an error bound using an error splitting model of approximation error and seek coefficients which minimise this. With minor modification this approach can also yield extrapolations. There are also potential applications to fault tolerance where new coefficients are required when a solution becomes unavailable due to a fault. We test the approach numerically on a scalar advection problem and compare with classical combinations from the literature. References

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