Gerrit Welper

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In this paper we propose and analyze stable variational formulations for convection diffusion problems starting from concepts introduced by Sangalli. We derive efficient and reliable a posteriori error estimators that are based on these formulations. The analysis of resulting adaptive solution concepts reveals partly unexpected phenomena related to the(More)
We propose a general framework for well posed variational formulations of linear unsymmetric operators, taking first order transport and evolution equations in bounded domains as primary orientation. We outline a general variational framework for stable discretizations of boundary value problems for these operators. To adaptively resolve anisotropic(More)
The central objective of this paper is to develop reduced basis methods for parameter dependent transport dominated problems that are rigorously proven to exhibit rate-optimal performance when compared with the Kolmogorov n-widths of the solution sets. The central ingredient is the construction of computationally feasible “tight” surrogates which in turn(More)
This paper considers the Dirichlet problem −div(a∇ua) = f on D, ua = 0 on ∂D, for a Lipschitz domain D ⊂ Rd, where a is a scalar diffusion function. For a fixed f , we discuss under which conditions a is uniquely determined and when a can be stably recovered from the knowledge of ua. A first result is that whenever a ∈ H1(D), with 0 < λ ≤ a ≤ Λ on D, and f(More)
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