Numerical analysis for applied mathematics, science, and engineering
Numerical analysis for applied mathematics, science, and engineering
Review: Monte Carlo methods for computing the capacitance of the unit cube
Mathematics and Computers in Simulation
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A new numerical value for the capacitance of each of the regular polyhedra is presented, obtained by employing a finite difference technique. In addition, a method is applied to the solutions of two of the polyhedra, the tetrahedron and the cube, to compute point-wise error estimatesa posteriori. Special considerations are discussed which are required to facilitate the computations of the solutions and the error estimates on these polyhedral domains, which exhibit extensive grid irregularities near the boundaries. An important feature of the error analysis method applied is that the results do not require the solution of a higher order h or p version.