For collocated SBP finite difference operators, discrete Helmholtz Hodge decompositions have an unavoidable remainder caused by grid oscillations, and iterative least-squares projections overcome this in practice.
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Discrete Vector Calculus and Helmholtz Hodge Decomposition for Classical Finite Difference Summation by Parts Operators
For collocated SBP finite difference operators, discrete Helmholtz Hodge decompositions have an unavoidable remainder caused by grid oscillations, and iterative least-squares projections overcome this in practice.