A fourth-order finite volume method for structural analysis

First, a number of simple test cases are designed to show that the method is exact for any polynomial up to the third order. After that, a beam subjected to thermal stresses and a cantilever fixed at one and loaded at the other end, for which analytical solutions exist, are analysed. In both latter cases, the method produces the exact analytical solution even on the coarsest grids. The fourth-order method results are compared with results obtained with a second-order method.