Adaptation based on interpolation errors for high order mesh refinement methods applied to conservation laws

Adaptive mesh refinement is nowadays a widely used tool in the numerical solution of hyperbolic partial differential equations. The algorithm is based on the numerical approximation of the solution of the equations on a hierarchical set of meshes with different resolutions. Among the different parts that compose an adaptive mesh refinement algorithm, the decision of which level of resolution is adequate for each part of the domain, i.e., the design of a refinement criterion, is crucial for the performance of the algorithm. In this work we analyze a refinement strategy based on interpolation errors, as a building block of a high order adaptive mesh refinement algorithm. We show that this technique, inspired by multiresolution algorithms, is competitive, in terms of the balance between accuracy of the solutions and computational time, against adaptation methods based on a gradient sensor.