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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 from the general laws of three-dimensional elasticity. We apply the framework for the so called Girkmann benchmark problem involving a spherical shell stiffened with a foot ring. In particular, we compare the accuracy of different reduced strain four-node elements in this context. We conclude that the performance of the bilinear shell finite elements depends on the mesh quality but reasonable accuracy of the quantities of interest of the Girkmann problem can be attained in contrast to earlier results obtained with general shell elements for the problem.
We propose and analyze a discretization scheme that combines the discontinuous Petrov-Galerkin and finite element methods. The underlying model problem is of general diffusion-advection-reaction type on bounded domains, with decomposition into two su
A method to simulate orthotropic behaviour in thin shell finite elements is proposed. The approach is based on the transformation of shape function derivatives, resulting in a new orthogonal basis aligned to a specified preferred direction for all el
We prove that the Scott-Vogelius finite elements are inf-sup stable on shape-regular meshes for piecewise quartic velocity fields and higher ($k ge 4$).
We show how two-dimensional mixed finite element methods that satisfy the conditions of finite element exterior calculus can be used for the horizontal discretisation of dynamical cores for numerical weather prediction on pseudo-uniform grids. This f
The notion of a tensor captures three great ideas: equivariance, multilinearity, separability. But trying to be three things at once makes the notion difficult to understand. We will explain tensors in an accessible and elementary way through the len