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We propose two classes of mixed finite elements for linear elasticity of any order, with interior penalty for nonconforming symmetric stress approximation. One key point of our method is to introduce some appropriate nonconforming…
The paper considers the general case of incompressible non-classical elasticity with small deformations and rotations. The thermodynamic stability is analysed for free energy density with three rotational degrees of freedom. Although the…
We rigorously prove the existence and the conformal invariance of scaling limits of the magnetization and multi-point spin correlations in the critical Ising model on arbitrary simply connected planar domains. This solves a number of…
This paper presents a pure complementary energy variational method for solving anti-plane shear problem in finite elasticity. Based on the canonical duality-triality theory developed by the author, the nonlinear/nonconex partial…
To begin with, we identify the equations of elastostatics in a Riemannian manifold, which generalize those of classical elasticity in the three-dimensional Euclidean space. Our approach relies on the principle of least energy, which asserts…
Many physical problems involving heterogeneous spatial scales, such as the flow through fractured porous media, the study of fiber-reinforced materials, or the modeling of the small circulation in living tissues -- just to mention a few…
In this paper we address the challenging problem of designing globally convergent estimators for the parameters of nonlinear systems containing a non-separable exponential nonlinearity. This class of terms appears in many practical…
We consider mixed finite element methods for linear elasticity where the symmetry of the stress tensor is weakly enforced. Both an a priori and a posteriori error analysis are given for several known families of methods that are uniformly…
We present a simple variational framework for planar elastica that enables distributed energies, such as gravitational loading or magnetic body torques, to be incorporated in a modular and unified manner. The formulation is based on…
The flexibility of the DPG methodology is exposed by solving the linear elasticity equations under different variational formulations, including some with non-symmetric functional settings (different infinite-dimensional trial and test…
A fundamental challenge in quantum physics is determining the ground-state properties of many-body systems. Whereas standard approaches, such as variational calculations, consist of writing down a wave function ansatz and minimizing over…
In this paper, we present an algorithm for the solution of the von Karman equations of elasticity theory and related problems. Our method of successive reconditioning is able to avoid convergence problems at any ratio of the nonlinear…
Poly-PL kinetic systems are kinetic systems consisting of nonnegative linear combinations of power law functions. In this contribution, we analyze these kinetic systems using two main approaches: (1) we define a canonical power law…
This article considers a model problem of elastoplasticity with linearly kinematic hardening and presents hp-finite element discretizations of two equivalent weak formulations each having their respective advantages. A mixed variational…
Linear and nonlinear resonant states can be restrictive: they exist at particular discrete states in frequency and/or elasticity, under particular (e.g., simple-harmonic) waveforms. In forced oscillators, this restrictiveness is an obstacle…
We use the worldline representation of field theory together with a variational approximation to determine the lowest bound state in the scalar Wick-Cutkosky model where two equal-mass constituents interact via the exchange of mesons.…
We derive the equations of nonlinear magnetoelastostatics using several variational formulations involving the mechanical deformation and an independent field representing the magnetic component. An equivalence is also discussed, modulo…
Starting from a model of nonlinear magnetoelasticity where magnetization is defined in the Eulerian configuration while elastic deformation is in the Lagrangean one, we rigorously derive a linearized model that coincides with the standard…
Structural transitions are invariably affected by lattice distortions. If the body is to remain crack-free, the strain field cannot be arbitrary but has to satisfy the Saint-Venant compatibility constraint. Equivalently, an incompatibility…
Astrophysical plasmas in the surrounding of compact objects and subject to intense gravitational and electromagnetic fields are believed to give rise to relativistic regimes. Theoretical and observational evidence suggest that magnetized…