Analysis of the order of accuracy for node-centered finite volume schemes (Q2271414)

The paper is concerned with the study of the order of accuracy of the node-centered finite volume methods. The behaviour of the node-centered finite volume method on a one-dimensional mesh is analyzed, using both hyperbolic and elliptic model problems. The scheme is formulated in terms of summation-by-parts operators and boundary conditions are imposed weakly using penalty terms. Numerical simulations are performed, and the results agree.