Browsing by Author "Sprungk, Björn"

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    On the convergence of adaptive stochastic collocation for elliptic partial differential equations with affine diffusion
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Eigel, Martin; Ernst, Oliver; Sprungk, Björn; Tamellini, Lorenzo
    Convergence of an adaptive collocation method for the stationary parametric diffusion equation with finite-dimensional affine coefficient is shown. The adaptive algorithm relies on a recently introduced residual-based reliable a posteriori error estimator. For the convergence proof, a strategy recently used for a stochastic Galerkin method with an hierarchical error estimator is transferred to the collocation setting.
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    Solving inverse problems with Bayes' theorem
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2022) Latz, Jonas; Sprungk, Björn
    The goal of inverse problems is to find an unknown parameter based on noisy data. Such problems appear in a wide range of applications including geophysics, medicine, and chemistry. One method of solving them is known as the Bayesian approach. In this approach, the unknown parameter is modelled as a random variable to reflect its uncertain value. Bayes' theorem is applied to update our knowledge given new information from noisy data.