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We present an administration technique for the bookkeeping of adaptive meshrefinement on (hyper-)rectangular meshes. Our technique is a unified approachfor h-refinement on 1-, 2- and 3D domains, which is easy to use and avoidstraversing the connectivity graph of the ancestry of mesh cells. Due to theemployed rectangular mesh structure, the identification of the siblings and theneighbouring cells is greatly simplified. The administration technique isparticularly designed for smooth meshes, where the smoothness is dynamicallyused in the matrix operations. It has a small memory footprint that makes itaffordable for a wide range of mesh resolutions over a large class of problems.We present three applications of this technique, one of which addressesh-refinement and its benefits in a 2D tumour growth and invasion problem.

An adaptive rectangular mesh administration and refinement technique with application in cancer invasion models