The Zlamal Approximation on a Sphere

Finite element approximation is often used to solve various problems in mathematical physics, such as boundary value problems. Previously, the authors considered the Courant approximation on a sphere. The Zlamal approximation on the plane gives smaller errors of approximation than the Courant approximation. This paper discusses a generalization of the Zlamal approximation on the plane and the Zlamal approximation on a sphere. The theoretical results are given for the Zlamal approximation on the plane and the Zlamal approximation on a sphere. The errors of approximation obtained with the Zlamal approximation and with the Courant approximation are compared. The results of the numerical experiments are given.