Browsing by Author "Fuhrer, Thomas"

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    A DPG method for shallow shells
    (SPRINGER HEIDELBERG, 2022) Fuhrer, Thomas; Heuer, Norbert; Niemi, Antti H.
    We develop and analyze a discontinuous Petrov-Galerkin method with optimal test functions (DPG method) for a shallow shell model of Koiter type. It is based on a uniformly stable ultraweak formulation and thus converges robustly quasi-uniformly. Numerical experiments for various cases, including the Scordelis-Lo cylindrical roof, elliptic and hyperbolic geometries, illustrate its performance. The built-in DPG error estimator gives rise to adaptive mesh refinements that are capable to resolve boundary and interior layers. The membrane locking is dealt with by raising the polynomial degree only of the tangential displacement trace variable.
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    Trace operators of the bi-Laplacian and applications
    (OXFORD UNIV PRESS, 2021) Fuhrer, Thomas; Haberl, Alexander; Heuer, Norbert
    We study several trace operators and spaces that are related to the bi-Laplacian. They are motivated by the development of ultraweak formulations for the bi-Laplace equation with homogeneous Dirichlet condition, but are also relevant to describe conformity of mixed approximations. Our aim is to have well-posed (ultraweak) formulations that assume low regularity under the condition of an L-2 right-hand side function. We pursue two ways of defining traces and corresponding integration-by-parts formulas. In one case one obtains a nonclosed space. This can be fixed by switching to the Kirchhoff-Love traces from Fiihrer et al. (2019, An ultraweak formulation of the Kirchhoff-Love plate bending model and DPG approximation. Math. Comp., 88, 1587-1619). Using different combinations of trace operators we obtain two well-posed formulations. For both of them we report on numerical experiments with the discontinuous Petrov-Galerkin method and optimal test functions. In this paper we consider two and three space dimensions. However, with the exception of a given counterexample in an appendix (related to the nonclosedness of a trace space) our analysis applies to any space dimension larger than or equal to two.
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    Trace operators of the bi-Laplacian and applications (vol 41, pg 1031, 2021)
    (OXFORD UNIV PRESS, 2021) Fuhrer, Thomas; Haberl, Alexander; Heuer, Norbert
    © The Author(s) 2020. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.The initial version of this article contained a number of formatting and minor language errors. These were the result of misinterpretation of requested corrections during typesetting. These errors have now been corrected.