Construction and investigation of the CPP (Cubic Polynomial Projection) method for the transport equation solving

The present paper is devoted to the construction of the (Cubic Polynomial Projection) method for solving the linear transport of neutral particles or unpolarized radiation on tetrahedra. The paper presents and proves estimates for the accuracy of the resulting numerical solution. The absorption coefficient is approximated by a constant value in the cell, the source is a second-degree polynomial in the cell, and the boundary condition is a third-degree polynomial on the faces. Under additional conditions, the method can reach the third order of convergence. The method is based on the characteristic properties of the transport equation, and in some sense, it is a generalization of the CIP (cubic-Interpolation pseudo-particle) method based on Hermitian interpolation in tetrahedra. The success of the method is ensured by the use of projection operators for constructing the scheme instead of the interpolation ones.