Abstract <p>A substantial disadvantage of standard numerical schemes with nonlinear flux correction is a severe deterioration in accuracy in areas of influence of shock waves: a drop in the order of convergence to the first order and a significant increase in solution errors. Combined numerical schemes make it possible to solve this problem and at the same time maintain the monotonicity of the calculated solution. The main element of any combined scheme is a nonmonotonic scheme, which has high accuracy in the areas of influence of shock waves. Two approaches to construct such schemes are compared. The first one is a local increase in the order of approximation in time using Runge–Kutta or Adams methods. The second one is a global a posteriori increase in the order of accuracy in time using Richardson methods. Schemes with a bicompact spatial approximation of the fourth order are compared using a test case for two-dimensional Euler equations. Its solution is a periodic smooth isentropic wave, which over time undergoes a gradient catastrophe and turns into a periodic shock wave. It is shown that the former approach is preferable if the problem can be solved by a nonmonotonic scheme completely, and meshes are moderately refined.</p>