Related papers: On H1, H(curl) and H(sym Curl) finite elements for…
In this paper, we review recent results on the conforming virtual element approximation of polyharmonic and elastodynamics problems. The structure and the content of this review is motivated by three paradigmatic examples of applications:…
Converging hierarchies of finite-dimensional semi-definite relaxations have been proposed for state-constrained optimal control problems featuring oscillation phe-nomena, by relaxing controls as Young measures. These semi-definite…
This work presents a finite element method for simulating dynamic processes that involve the coupled evolution of dislocation motion and crack propagation. The method numerically solves the Concurrent Atomistic-Continuum (CAC) formulation…
We develop and demonstrate the first general computational tool for finite deformation static and dynamic dislocation mechanics. A finite element formulation of finite deformation (Mesoscale) Field Dislocation Mechanics theory is presented.…
We introduce a family of hybrid discretisations for the numerical approximation of optimal control problems governed by the equations of immiscible displacement in porous media. The proposed schemes are based on mixed and discontinuous…
The finite-element approach to lattice field theory is both highly accurate (relative errors $\sim 1/N^2$, where $N$ is the number of lattice points) and exactly unitary (in the sense that canonical commutation relations are exactly…
With the regular decomposition technique, we decompose the space $\mathbf{H}_0^s(\mathbf{curl}; \Omega)$ into the sum of a vector potential space and the gradient of a scalar space, both possessing higher regularity. Based on this new high…
In conventional spectral/finite element methods, the triangulation/quadrilateralization of the domain produces many interior edges which require additional DOF. What if we could directly use the original hull without going to…
Nonlocal material response distinctively changes the optical properties of nano-plasmonic scatterers and waveguides. It is described by the nonlocal hydrodynamic Drude model, which -- in frequency domain -- is given by a coupled system of…
This article introduces a new 3D magnetohydrodynamic (MHD) equilibrium solver, based on the concept of admissible variations of B, p that allows for magnetic relaxation of a magnetic field in a perturbed/non-minimum energy state to a lower…
We introduce a perturbation expansion for athermal systems that allows an exact determination of displacement fields away from the crystalline state as a response to disorder. We show that the displacement fields in energy minimized…
We address combinatorial problems that can be formulated as minimization of a partially separable function of discrete variables (energy minimization in graphical models, weighted constraint satisfaction, pseudo-Boolean optimization, 0-1…
We construct several smooth finite element spaces defined on three--dimensional Worsey--Farin splits. In particular, we construct $C^1$, $H^1(\curl)$, and $H^1$-conforming finite element spaces and show the discrete spaces satisfy local…
This article surveys research on the application of compatible finite element methods to large scale atmosphere and ocean simulation. Compatible finite element methods extend Arakawa's C-grid finite difference scheme to the finite element…
In this work, we study the accuracy and efficiency of hierarchical matrix ($\mathcal{H}$-matrix) based fast methods for solving dense linear systems arising from the discretization of the 3D elastodynamic Green's tensors. It is well known…
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…
Since the 1960's the finite element method emerged as a powerful tool for the numerical simulation of countless physical phenomena or processes in applied sciences. One of the reasons for this undeniable success is the great versatility of…
Highly spinning classical strings on RxS^3 are described by the Landau-Lifshitz model or equivalently by the Heisenberg ferromagnet in the thermodynamic limit. The spectrum of this model can be given in terms of spectral curves. However, it…
We study the complete set of flavor changing hyperon axial current matrix elements at small momentum transfer. Using partially quenched heavy baryon chiral perturbation theory, we derive the chiral and momentum behavior of the axial and…
The design of mixed finite element methods in linear elasticity with symmetric stress approximations has been a longstanding open problem until Arnold and Winther designed the first family of mixed finite elements where the discrete stress…