Finite element approximation of a semilinear elliptic problem with a singular nonlinearity
The \(H^1\) and \(L^\infty\) error bounds for finite element approximation of the equation \[ -\Delta u=cu^{-\nu}, \quad c>0,\;\nu>0 \] are proved. The effect of numerical integration of the nonlinear term is analyzed. Numerical results for one dimension are presented.
scientific article; zbMATH DE number 1310651