Penalty-combined method and applications in solving elliptic problems with singularities

Abstract

The simplest penalty technique is proposed for matching the Ritz-Galerkin and finite elements methods in solving elliptic problems with multiple singularities. The advantage of this method over the nonconforming combination is its simplicity, without dealing with direct constraints. Error bounds are provided to guide the choice of the penalty constant P c. Moreover, when P c is chosen properly large, the numerical solutions from the penalty combined method will approach those from the nonconforming combination. Numerical experiments are carried out for Motz's problem to justify the proposed coupling technique. This technique is also applied to the study of potential flow of wind over buildings where there exist multiple singularities and multiple coupling interfaces among different numerical methods. On the whole, the penalty combined method is useful for solving complicated engineering problems.