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High-order finite-difference methods for Poisson's equation
1974
Mathematics of Computation
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Finite-difference approximations to the three boundary value problems for Poisson's equation are given with discretization errors of 0(h3) for the mixed boundary value problem, 0(A3|ln h\) for the Neumann problem and 0(h*) for the Dirichlet problem, respectively. These error bounds are an improvement upon similar results obtained by Bramble and Hubbard; moreover, all resulting coefficient matrices are of positive type. Again, under general assumptions, a solution, unique except for an additive
doi:10.1090/s0025-5718-1974-0362936-2
fatcat:3lqll63cgvdmzjvqmi7idvj2di