Finite element approximation for a div-rot system with mixed boundary conditions in non-smooth plane domains

Abstract

The authors examine a finite element method for the numerical approximation of the solution to a div-rot system with mixed boundary conditions in bounded plane domains with piecewise smooth boundary. The solvability of the system both in an infinite and finite dimensional formulation is proved. Piecewise linear element fields with pointwise boundary conditions are used and their approximation properties are studied. Numerical examples indicating the accuracy of the method are given.