Related papers: A locally mass conserving quadratic velocity, line…
We formulate a novel numerical method suitable for the solution of topology optimization problems in solid mechanics. The most salient feature of the new approach is that the space and time discrete equations of the numerical method can be…
We model a 3D turbulent fluid, evolving toward a statistical equilibrium, by adding to the equations for the mean field $(v, p)$ a term like $-\alpha \nabla\cdot(\ell(x) D v_t)$. This is of the Kelvin-Voigt form, where the Prandtl mixing…
We consider a mixed finite element method for approximating the solution of nearly incompressible elasticity and Stokes equations. The finite element method is based on quadrilateral and hexahedral triangulation using primal and dual…
In this research paper, the problem of optimization of a quadratic form over the convex hull generated by the corners of hypercube is attempted and solved. It is reasoned that under some conditions, the optimum occurs at the corners of…
Using the Laughlin's argument on a torus with two pin-holes, we numerically demonstrate that the discontinuities of the center-of-mass work well as an invariant of the pumping phenomena during the process of the flux-attachment, trading the…
We consider the mass conserving Allen-Cahn equation proposed in \cite{Bra-Bre}: the Lagrange multiplier which ensures the conservation of the mass contains not only nonlocal but also local effects (in contrast with \cite{Che-Hil-Log}). As a…
We develop a covariant variational framework for relativistic electromagnetic continua (fluids and solid) based on Hamilton's principle formulated directly in the material description. The approach extends the geometric theory of…
A local convergence rate is established for a Gauss orthogonal collocation method applied to optimal control problems with control constraints. If the Hamiltonian possesses a strong convexity property, then the theory yields convergence for…
In this paper, the stabilized finite element approximation of the Stokes eigenvalue problems is considered for both the two-field (displacement-pressure) and the three-field (stress-displacement-pressure) formulations. The method presented…
The present paper aims at the investigation of the global stability of large solutions to the compressible Navier-Stokes equations in the whole space. Our main results and innovations can be concluded as follows: Under the assumption that…
Although Regge finite element functions are not continuous, useful generalizations of nonlinear derivatives like the curvature, can be defined using them. This paper is devoted to studying the convergence of the finite element lifting of a…
We formulate and prove a periodic analog of Maxwell's theorem relating stressed planar frameworks and their liftings to polyhedral surfaces with spherical topology. We use our lifting theorem to prove deformation and rigidity-theoretic…
A stable finite element scheme that avoids pressure oscillations for a three-field Biot's model in poroelasticity is considered. The involved variables are the displacements, fluid flux (Darcy velocity), and the pore pressure, and they are…
In this paper a higher-order mixed finite element method for elastoplasticity with linear kinematic hardening is analyzed. Thereby, the non-differentiability of the involved plasticity functional is resolved by a Lagrange multiplier leading…
The inclusion of rigid elements into elastic composites may lead to superior mechanical properties for the equivalent elastic continuum, such as, for instance, extreme auxeticity. To allow full exploitation of these properties, a tool for…
We develop arbitrarily high-order, stationarity-preserving stabilized finite element methods for multidimensional nonlinear hyperbolic balance laws on Cartesian grids. We aim at approximating all the steady states of the problem at hand,…
We illustrate a broken Hardy inequality on discontinuous finite element spaces, blowing up with a logarithmic factor with respect to the meshes size. This is motivated by numerical analysis for the strain gradient elasticity with natural…
In [21] the evolution of hypersurfaces in $\mathbb{R}^{n+1}$ with normal speed equal to a power $k>1$ of the mean curvature is considered and the levelset solution $u$ of the flow is obtained as the $C^0$-limit of a sequence $u^{\epsilon}$…
The present paper aims at representing an improvement of the result in [2], where a strong unique continuation property and a description of the local behaviour around the edge of a crack for solutions to an elliptic problem are…
A decade ago, a Lagrangian density has been proposed by the author where only the local symmetries of the Lorentz subgroup of (A)ds group is retained. This formalism has been found to produce some results encompassing that of standard…