A Two-Grid Approximation of an Interface Problem for the Nonlinear Poisson-Boltzmann Equation
We present a robust and efficient numerical method for solution of an interface problem for a generalization of the Poisson-Boltzmann equation, arising in molecular biophysics. The differential problem is solved by FEM (finite element method) technique on two (coarse and fine) subspaces. The solution of the nonlinear system of algebraic equations on the fine mesh is reduced to the solution on two small (one linear and one nonlinear) systems on the coarse grid and a large linear one on the fine grid. It is shown, both theoretically and numerically, that the coarse space can be extremely coarse and still achieve asymptotically optimal approximation.
KeywordsConvergence Rate Coarse Grid Coarse Mesh Interface Problem Coarse Space
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