On the construction of essentially non-oscillatory finite volume approximations to hyperbolic conservation laws on general triangulations: Polynomial recovery, accuracy and stencil selection

We develop essentially non-oscillatory (ENO) finite volume methods on conforming triangulations for the numerical solution of hyperbolic conservation laws. Besides theoretical results concerning the recovery of data from cell averages. we give a description of practicable algorithms for the stencil selection to recover polynomials of arbitrary degree. Extensive numerical tests confirm the accuracy of the methods which can be theoretically predicted.