Stable Dynamical Adaptive Mesh Refinement

Abstract We consider accurate and stable interpolation procedures for numerical simulations utilizing time dependent adaptive meshes. The of solution values between meshes is considered as a transmission problem with respect to the underlying semi-discretized equations, theoretical framework using inner product preserving operators developed, which allows both explicit implicit implementations. theory supplemented experiments demonstrating practical benefits new framework. For this purpose, have been designed be used multi-block finite difference schemes involving non-collocated, moving interfaces.