The maximum angle condition in the finite element method for monotone problems with applications in magnetostatics (Q1899134)

In analyzing two-dimensional magnetic fields in electrical machines it is important to solve a special quasilinear elliptic equation in a disk \(|x |< r_1\) that contains two smaller disks \(|x |< r_2\) and \(|x|< r_3\) where \(r_2 - r_3 > 0\) and small. The author shows that it is possible to use triangulations such that they contain only triangles \(T\) with the maximal angle \(\gamma_T \leq \gamma^* < \pi\) (the small angles are allowed what is of importance for the narrow subdomain). If the solution is piecewise of class \(H^2\) (in each of the three subdomains) then the error estimate of type \(|z|_{H^1(\widehat{\Omega}_h)} = O(h)\) is obtained.