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Sobolev gradient type preconditioning is proposed for the numerical solution of the electrostatic potential equation. A constructive representation of the gradients leads to efficient Laplacian preconditioners in the iteration thanks to the available fast Poisson solvers. Convergence is then verified for the corresponding sequence in Sobolev space, implying mesh independent convergence results for the discretized problems. A particular study is devoted to the case of a ball: due to the radialdoi:10.1016/j.camwa.2005.08.011 fatcat:uskglbrkmzbarlo5dy4ascvgpu