Related papers: Stable mixed element schemes for plate models on m…
It is shown how mixed finite element methods for symmetric positive definite eigenvalue problems related to partial differential operators can provide guaranteed lower eigenvalue bounds. The method is based on a classical compatibility…
A mechanical model and numerical method for the simultaneous analysis of Reissner-Mindlin shells with geometries implied by a continuous set of level sets (isosurfaces) over some three-dimensional bulk domain is presented. A…
A dynamic linear thermo-poroelasticity model, containing inertial and relaxation terms with second-order time derivatives, is investigated in this paper. The mathematical and numerical analysis of this model is performed in the frequency…
In this work, we present and analyze a fully-mixed finite element scheme for the dynamic poroelasticity problem in the low-frequency regime. We write the problem as a four-field, first-order, hyperbolic system of equations where the…
In this work we study a strongly coupled system between the equation of plates with fractional rotational inertial force $\kappa(-\Delta)^\beta u_{tt}$ where the parameter $0 <\beta\leq 1$ and the equation of an electrical network…
The wide adoption of composite structures in the aerospace industry requires reliable numerical methods to account for the effects of various damage mechanisms, including delamination. Cohesive elements are a versatile and physically…
We derive a residual a posteriori estimator for the Kirchhoff plate bending problem. We consider the problem with a combination of clamped, simply supported and free boundary conditions subject to both distributed and concentrated (point…
An effective model is identified for thin perfectly plastic plates whose microstructure consists of the periodic assembling of two elastoplastic phases, as the periodicity parameter converges to zero. Assuming that the thickness of the…
For Kichhoff-Love shell problems a new mixed formulation solely based on standard $H^1$ spaces is presented. This allows for flexibility in the construction of discretization spaces, e.g., standard $C^0$-coupling of multi-patch isogeometric…
Symplectic mappings of the plane serve as key models for exploring the fundamental nature of complex behavior in nonlinear systems. Central to this exploration is the effective visualization of stability regimes, which enables the…
In this work, we propose a novel formulation for the solution of partial differential equations using finite element methods on unfitted meshes. The proposed formulation relies on the discrete extension operator proposed in the aggregated…
We study mixed finite element methods for the rotating shallow water equations with linearized momentum terms but nonlinear drag. By means of an equivalent second-order formulation, we prove long-time stability of the system without energy…
We observe a dramatic lack of robustness of the DPG method when solving problems on large domains and where stability is based on a Poincar\'e-type inequality. We show how robustness can be re-established by using appropriately scaled test…
We consider a finite element discretization for the dual Rudin--Osher--Fatemi model using a Raviart--Thomas basis for $H_0 (\mathrm{div};\Omega)$. Since the proposed discretization has splitting property for the energy functional, which is…
In this paper, a unified family, for any $n\geqslant 2$ and $1\leqslant k\leqslant n-1$, of nonconforming finite element schemes are presented for the primal weak formulation of the $n$-dimensional Hodge-Laplace equation on $H\Lambda^k\cap…
Two types of finite element spaces on triangles are constructed for div-div conforming symmetric tensors. Besides the normal-normal continuity, the stress tensor is continuous at vertices and another trace involving combination of…
Exotic behaviour of mechanical metamaterials often relies on an internal transformation of the underlying microstructure triggered by its local instabilities, rearrangements, and rotations. Depending on the presence and magnitude of such a…
We consider the stability of synchronized states (including equilibrium point, periodic orbit or chaotic attractor) in arbitrarily coupled dynamical systems (maps or ordinary differential equations). We develop a general approach, based on…
The evolution of multivariant patterns in thin plates of magnetic shape memory materials with an applied magnetic field was studied theoretically. A geometrical domain-model is considered composed of straight stripe-like martensite variants…
In this paper, we develop a virtual element method (VEM) of high order to solve the fourth order plate buckling eigenvalue problem on polygonal meshes. We write a variational formulation based on the Kirchhoff-Love model depending on the…