Browsing by Author "Niemi, Antti H."

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    A Discontinuous Petrov–Galerkin Method for Reissner–Mindlin Plates
    (2023) Führer, Thomas; Heuer, Norbert; Niemi, Antti H.
    We present a discontinuous Petrov–Galerkin method with optimal test functions for the Reissner–Mindlin plate bending model. Our method is based on a variational formulation that utilizes a Helmholtz decomposition of the shear force. It produces approximations of the primitive variables and the bending moments. For any canonical selection of boundary conditions the method converges quasi-optimally. In the case of hard-clamped convex plates, we prove that the lowest-order scheme is locking free. Several numerical experiments confirm our results.
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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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    AN ULTRAWEAK FORMULATION OF THE KIRCHHOFF-LOVE PLATE BENDING MODEL AND DPG APPROXIMATION
    (2019) Führer, Thomas; Heuer, Norbert; Niemi, Antti H.