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

The scaled boundary nite element method, alias the consistent in nitesimal nite element cell method, is developed starting from the di usion equation. Only the boundary of the medium is discretized with surface nite elements yielding a reduction of the spatial dimension by one. No fundamental solution is necessary, and thus no singular integrals need to be evaluated. Essential and natural boundary conditions on surfaces and conditions on interfaces between di erent materials are enforced exactly without any discretization. The solution of the function in the radial direction is analytical. This method is thus exact in the radial direction and converges to the exact solution in the nite element sense in the circumferential directions. The semi- analytical solution inside the domain leads to an e cient procedure to calculate singularities accurately without discretization in the vicinity of the singular point. For a bounded medium symmetric steady-state sti ness and mass matrices with respect to the degrees of freedom on the boundary result without any additional assumption