28 citations · 48 across the 16 of their papers we have counts for
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math.NA2014★ 1 cited
A Reduced Basis Method for Parabolic Partial Differential Equations with Parameter Functions and Application to Option Pricing
Antonia Mayerhofer, Karsten Urban
We consider the Heston model as an example of a parameterized parabolic partial differential equation. A space-time variational formulation is derived that allows for parameters in…
math.NA2014★ 11 cited
Reduced Basis Methods Based Upon Adaptive Snapshot Computations
Mazen Ali, Kristina Steih, Karsten Urban
We use asymptotically optimal \emph{adaptive} numerical methods (here specifically a wavelet scheme) for snapshot computations within the offline phase of the Reduced Basis Method…
math.NA2014★ 1 cited
An efficient space-time adaptive wavelet Galerkin method for time-periodic parabolic partial differential equations
Sebastian Kestler, Kristina Steih, Karsten Urban
We introduce a multitree-based adaptive wavelet Galerkin algorithm {for} space-time discretized linear parabolic partial differential equations, focusing on time-periodic problems.…