Study of the effectiveness of curved finite elements on the example of solving a magnetostatic problem

The work studies the effectiveness of using curved finite elements in finite element modeling. The study was made on the example of solving a magnetostatic problem by means of a finite element method stated using two scalar potentials. As a rule, in applied problems researchers have to work on a computational domain with curved boundary. If finite elements with only rectilinear boundaries are used, the order of solution approximation with increase in the order of basis functions will be limited by the approximation order of the curved boundary. The work offers a short review of the object domain: description of a mathematical model of a magnetostatic problem stated using two scalar potentials; covers a problem of calculation evaluation of a potential break; examines approaches to increasing the order of finite elements. The work solves a problem of finite element modeling using basis functions of various orders on rectilinear and curved finite elements and shows how an increase of the order of finite elements affects the accuracy of the obtained solution and the convergence order of the method.