Combined triangular FV‐triangular FE method for nonlinear convection‐diffusion problems

Abstract

AbstractThe paper is concerned with the analysis of the combined finite element ‐ finite volume method for the solution of nonstationary nonlinear convection‐diffusion problems. Here a special version of this technique is analyzed, combining conforming piecewise linear triangular elements, used for the discretization of diffustion terms, with triangular finite volumes for the approximation of nonlinear convective terms. The finite volume and finite element meshes have to be of the same size, but their shape can be practically independent. In the paper, the error estimates of this method are proven under the assumptions that the finite element meshes are shape regular, the size of the finite element and finite volume meshes are equivalent and the exact solution is sufficiently regular. Theoretical analysis is accompanied by numerical experiments, showing the optimality of the derived error estimates.