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The numerical approximation of solutions of parametric or stochastichyperbolic PDEs is still a serious challenge. Because of shock singularities,most methods from the elliptic and parabolic regime, such as reduced basismethods, POD or polynomial chaos expansions, show a poor performance. Recently,Welper [Interpolation of functions with parameter dependent jumps bytransformed snapshots. SIAM Journal on Scientific Computing, 39(4):A1225-A1250,2017] introduced a new approximation method, based on the alignment of the jumpsets of the snapshots. If the structure of the jump sets changes withparameter, this assumption is too restrictive. However, these changes aretypically local in parameter space, so that in this paper, we explore $h$ and$hp$-adaptive methods to resolve them. Since local refinements do not scale tohigh dimensions, we introduce an alternative "tensorized" adaption method.

$h$ and $hp$-adaptive Interpolation by Transformed Snapshots for Parametric and Stochastic Hyperbolic PDEs