On the Use of Monotonicity-Preserving Interpolatory Techniques in Multilevel Schemes for Balance Laws

Cost-effective multilevel techniques for homogeneous hyperbolic conservation laws are very successful in reducing the computational cost associated to high resolution shock capturing numerical schemes. Because they do not involve any special data structure, and do not induce savings in memory requirements, they are easily implemented on existing codes and are recommended for 1D and 2D simulations when intensive testing is required. The multilevel technique can also be applied to balance laws, but in this case, numerical errors may be induced by the technique. We present a series of numerical tests that point out that the use of monotonicity-preserving interpolatory techniques eliminates the numerical errors observed when using the usual 4-point centered Lagrange interpolation, and leads to a more robust multilevel code for balance laws, while maintaining the efficiency rates observed for hyperbolic conservation laws.