The scaled boundary finite element method-alias consistent infinitesimal finite element cell method-for diffusion

The scaled boundary finite element method, alias the consistent infinitesim al finite element cell method, is developed starting from the diffusion equ ation. Only the boundary of the medium is discretized with surface finite e lements yielding a reduction of the spatial dimension by one. No fundamenta l solution is necessary, and thus no singular integrals need to be evaluate d. Essential and natural boundary conditions on surfaces and conditions on interfaces between different materials are enforced exactly without any dis cretization. The solution of the function in the radial direction is analyt ical. This method is thus exact in the radial direction and converges to th e exact solution in the finite element sense in the circumferential directi ons. The semianalytical solution inside the domain leads to an efficient pr ocedure to calculate singularities accurately without discretization in the vicinity of the singular point. For a bounded medium symmetric steady-stat e stiffness and mass matrices with respect to the degrees of freedom on the boundary result without any additional assumption. Copyright (C) 1999 John Wiley & Sons, Ltd.