Abstract:In this paper the problem −div(a(x,y)∇u)= f with Dirichlet boundary conditions on a square is solved iteratively with high accuracy for u and ∇u using a new scheme called "hermitian box-scheme". The design of the scheme is based on a "hermitian box", combining the approximation of the gradient by the fourth order hermitian derivative, with a conservative discrete formulation on boxes of length 2h. The iterative technique is based on the repeated solution by a fast direct method of a discrete Poisson equation o… Show more
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