Related papers: Convergence analysis of a finite element approxima…
In this article, the piecewise-linear finite element method (FEM) is applied to approximate the solution of time-fractional diffusion equations on bounded convex domains. Standard energy arguments do not provide satisfactory results for…
The dynamics of disordered two-dimensional systems is much less understood than the dynamics of disordered chains, mainly due to the lack of appropriate numerical methods. We demonstrate that a single-trajectory version of the fermionic…
We analyze the convergence of the electron density and relative energy with respect to a perfect crystal of a class of volume defects that are compactly contained along one direction while being of infinite extent along the other two using…
We develop a microscopic approach to the consistent construction of the kinetic theory of dilute weakly ionized gases of hydrogen-like atoms. The approach is based on the framework of the second quantization method in the presence of bound…
Regardless of the development of various finite element methods for fluid-structure interaction (FSI) problems, optimal-order convergence of finite element discretizations of the FSI problems in the $L^\infty(0,T;L^2)$ norm has not been…
In this work we analyze the variational problem emerging from the Gutzwiller approach to strongly correlated systems. This problem comprises the two main steps: evaluation and minimization of the ground state energy $W$ for the postulated…
Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…
With this contribution, we shed light on the relation between the discrete adjoints of multistep backward differentiation formula (BDF) methods and the solution of the adjoint differential equation. To this end, we develop a…
We develop a refined Frozen Gaussian approximation (FGA) for the fractional Schr\"odinger equation in the semi-classical regime, where the solution exhibits rapid oscillations as the scaled Planck constant $\varepsilon$ becomes small. Our…
We study the minimization of the non-convex and non-differentiable objective function $v \mapsto \mathrm{E} ( \| X - v \| \| X + v \| - \| X \|^2 )$ in $\mathbb{R}^p$. In particular, we show that its minimizers recover the first principal…
We analyze the dynamics of an algorithm for approximate inference with large Gaussian latent variable models in a student-teacher scenario. To model nontrivial dependencies between the latent variables, we assume random covariance matrices…
We study simple approximations to fractional Gaussian noise and fractional Brownian motion. The approximations are based on spectral properties of the noise. They allow one to consider the noise as the result of fractional…
We prove a functional limit theorem for vector-valued functionals of the fractional Ornstein-Uhlenbeck process, providing the foundation for the fluctuation theory of slow/fast systems driven by such a noise. Our main contribution is on the…
In this paper we describe a computational model for the simulation of fluid-structure interaction problems based on a fictitious domain approach. We summarize the results presented over the last years when our research evolved from the…
We consider the numerical construction of minimal Lagrangian graphs, which is related to recent applications in materials science, molecular engineering, and theoretical physics. It is known that this problem can be formulated as an…
We study a large deviation functional of density fluctuation by analyzing stochastic non-linear diffusion equations driven by the difference between the densities fixed at the boundaries. By using a fundamental equality that yields the…
We provide a minimax optimal estimation procedure for F and W in matrix valued linear models Y = F W + Z where the parameter matrix W and the design matrix F are unknown but the latter takes values in a known finite set. The proposed finite…
We present a finite element discretization of a non-linear diffusion equation used in the field of critical phenomena and, more recently, in the context of Dynamic Density Functional Theory. The discretized equation preserves the structure…
The numerical approximation of the solution to a stochastic partial differential equation with additive spatial white noise on a bounded domain is considered. The differential operator is assumed to be a fractional power of an integer order…
Connecting short time microscopic dynamics with long time hydrodynamics in strongly correlated quantum systems is one of the outstanding questions. In particular, it is very difficult to determine various hydrodynamic coefficients like the…