8 papers
A DPG method for the circular arch problem
Norbert Heuer, Antti H. Niemi
We consider an elastic model for a circular arch that incorporates membrane, transverse shear, and bending effects. The central line of the arch is partitioned into elements, and a…
A DPG method for Reissner-Mindlin plates
Thomas Führer, Norbert Heuer, Antti H. Niemi
We present a discontinuous Petrov-Galerkin (DPG) method with optimal test functions for the Reissner-Mindlin plate bending model. Our method is based on a variational formulation t…
A DPG method for shallow shells
Thomas Führer, Norbert Heuer, Antti H. Niemi
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…
An ultraweak formulation of the Kirchhoff-Love plate bending model and DPG approximation
Thomas Führer, Norbert Heuer, Antti H. Niemi
We develop and analyze an ultraweak variational formulation for a variant of the Kirchhoff-Love plate bending model. Based on this formulation, we introduce a discretization of the…
Benchmark Computations of stresses in a spherical dome with shell finite elements
Antti H. Niemi
We present a computational framework for analysing thin shell structures using the finite element method. The framework is based on a mesh-dependent shell model which we derive fro…
Analysis of the Discontinuous Petrov-Galerkin Method with Optimal Test Functions for the Reissner-Mindlin Plate Bending Model
Victor M. Calo, Nathaniel O. Collier, Antti H. Niemi
We analyze the discontinuous Petrov-Galerkin (DPG) method with optimal test functions when applied to solve the Reissner-Mindlin model of plate bending. We prove that the hybrid va…
On the Shape Optimization of Flapping Wings and their Performance Analysis
Mehdi Ghommem, Nathan Collier, Antti H. Niemi +1
The present work is concerned with the shape optimization of flapping wings in forward flight. The analysis is performed by combining a gradient-based optimizer with the unsteady v…
Automatically Stable Discontinuous Petrov-Galerkin Methods for Stationary Transport Problems: Quasi-Optimal Test Space Norm
Antti H. Niemi, Nathaniel O. Collier, Victor M. Calo
We investigate the application of the discontinuous Petrov-Galerkin (DPG) finite element framework to stationary convection-diffusion problems. In particular, we demonstrate how th…