Related papers: Benchmark Computations of stresses in a spherical …
We consider the singularly perturbed fourth-order boundary value problem $\varepsilon ^{2}\Delta ^{2}u-\Delta u=f $ on the unit square $\Omega \subset \mathbb{R}^2$, with boundary conditions $u = \partial u / \partial n = 0$ on $\partial…
We develop a new finite element method for solving planar elasticity problems involving of heterogeneous materials with a mesh not necessarily aligning with the interface of the materials. This method is based on the `broken'…
Partition of unity methods, such as the extended finite element method (XFEM) allow discontinuities to be simulated independently of the mesh [1]. This eliminates the need for the mesh to be aligned with the discontinuity or cumbersome…
A robust $hp$-adaptive finite element framework is presented for the investigation of static cracks in materials characterized by complex, pointwise density variations. Within such heterogeneous media, the equilibrium equation governed by…
We present new rectangular mixed finite elements for linear elasticity. The approach is based on a modification of the Hellinger-Reissner functional in which the symmetry of the stress field is enforced weakly through the introduction of a…
In the present paper, a new parabolic shear deformation beam theory is developed and applied to investigate the bending behavior of functionally graded (FG) sandwich curved beam. The present theory is exploited to satisfy parabolic…
In this paper, we analyze the supercloseness property of the streamline diffusion finite element method (SDFEM) on Shishkin triangular meshes, which is different from one in the case of rectangular meshes. The analysis depends on integral…
We present an implementation of a fully variational formulation of an immersed method for fluid-structure interaction problems based on the finite element method. While typical implementation of immersed methods are characterized by the use…
In this paper, the numerical approximation of isometric deformations of thin elastic shells is discussed. To this end, for a thin shell represented by a parametrized surface, it is shown how to transform the stored elastic energy for an…
The critical buckling characteristics of hydrostatically pressurized complete spherical shells filled with an elastic medium are demonstrated. A model based on small deflection thin shell theory, the equations of which are solved in…
We develop a robust cut finite element method for a model of diffusion in fractured media consisting of a bulk domain with embedded cracks. The crack has its own pressure field and can cut through the bulk mesh in a very general fashion.…
In this paper, we formulate, analyse and implement the discrete formulation of the Brinkman problem with mixed boundary conditions, including slip boundary condition, using the Nitsche's technique for virtual element methods. The divergence…
In this paper, size-dependent dynamic responses of small-size frames are modelled by stress-driven nonlocal elasticity and assessed by a consistent finite-element methodology. Starting from uncoupled axial and bending differential…
We present a new stability and convergence analysis for the spatial discretization of a time-fractional Fokker--Planck equation in a convex polyhedral domain, using continuous, piecewise-linear, finite elements. The forcing may depend on…
We propose a novel cut finite element method for the numerical solution of the Biot system of poroelasticity. The Biot system couples elastic deformation of a porous solid with viscous fluid flow and commonly arises on domains with complex…
The paper is concerned with the development of efficient and accurate solution procedures for the isogeometric boundary element method (BEM) when applied to problems that contain inclusions that have elastic properties different to the…
In this paper we establish the convergence of a numerical scheme based, on the Finite Element Method, for a time-independent problem modelling the deformation of a linearly elastic elliptic membrane shell subjected to remaining confined in…
We consider a surface Stokes problem in stream function formulation on a simply connected oriented surface $\Gamma \subset \mathbb{R}^3$ without boundary. This formulation leads to a coupled system of two second order scalar surface partial…
We consider numerical simulation of the isotropic elastic wave equations arising from seismic applications with non-trivial land topography. The more flexible finite element method is applied to the shallow region of the simulation domain…
Finite difference method and pseudo-spectral method have been widely used in the numerical relativity to solve the Einstein equations. As the third major category method to solve partial differential equations, finite element method is much…