Infinite element method for elliptic problems (Q1201566)

The purpose of this paper is to introduce an infinite element method which is valid for general elliptic equations. This method can also be applied to higher-order equations or to some nonlinear problems. For solutions which possess singularities, singular numerical solutions can be obtained with a small scale of computation; besides, it is unnecessary to know the order of singularity of the solutions or the analytic expressions of particular solutions in advance. Two meshes, infinite and finite, are used to calculate the numerical solution of the boundary value problem on an \(L\)-shaped domain \(\Omega\), \(-\nabla(a(x)\nabla u)=f\), \(u|_{\partial\Omega}=g\).