Related papers: Far-field displacement singularity elimination for…
Time discretization along with space discretization is important in the numerical simulation of subsurface flow applications for long run. In this paper, we derive theoretical convergence error estimates in discrete-time setting for…
Starting from smooth initial data, we investigate the complex-time analytic structure of the one-dimensional Hou--Luo (HL) model, a wall approximation of the three-dimensional axisymmetric Euler equations. While the finite-time blow-up in…
The quantum dissipative dynamics of a tunneling process through double barrier structures is investigated on the basis of a rigorous treatment for the first time. We employ a Caldeira-Leggett Hamiltonian with an effective potential…
As a phase space language for quantum mechanics, the Wigner function approach bears a close analogy to classical mechanics and has been drawing growing attention, especially in simulating quantum many-body systems. However, deterministic…
In this note, we consider the nonlocal Cahn-Hilliard equation with constant mobility and singular potential in three dimensional bounded and smooth domains. Given any global solution (whose existence and uniqueness are already known), we…
We propose a space-time scheme that combines an unfitted finite element method in space with a discontinuous Galerkin time discretisation for the accurate numerical approximation of parabolic problems with moving domains or interfaces. We…
The Vlasov-Fokker-Planck equation describes the evolution of the probability density of the position and velocity of particles under the influence of external confinement, interaction, friction, and stochastic force. It is well-known that…
The problem of time and the quantization of three dimensional gravity in the strong coupling regime is studied following path integral methods. The time is identified with the volume of spacetime. We show that the effective action describes…
This paper presents a new and unified approach to the derivation and analysis of many existing, as well as new discontinuous Galerkin methods for linear elasticity problems. The analysis is based on a unified discrete formulation for the…
The convergence analysis of a third-order scheme for the highly nonlinear Landau-Lifshitz-Gilbert equation with a non-convex constraint is considered. In this paper, we first present a fully discrete semi-implicit method for solving the…
Achieving strongly symmetric stress approximations for linear elasticity problems in high-contrast media poses a significant computational challenge. Conventional methods often struggle with prohibitively high computational costs due to…
The tractions that cells exert on a gel substrate from the observed displacements is an increasingly attractive and valuable information in biomedical experiments. The computation of these tractions requires in general the solution of an…
A recent analysis of real general relativity based on multisymplectic techniques has shown that boundary terms may occur in the constraint equations, unless some boundary conditions are imposed. This paper studies the corresponding form of…
Uniqueness of solutions in the linear theory of non-singular dislocations, studied as a special case of plasticity theory, is examined. The status of the classical, singular Volterra dislocation problem as a limit of plasticity problems is…
We study flat Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) models with a perfect fluid matter source and a scalar field minimally coupled to matter with power-law-exponential \textquotedblleft hybrid\textquotedblright potential. Using…
The full nonlinear dissipative quasigeostrophic model is shown to have a unique temporally almost periodic solution when the wind forcing is temporally almost periodic under suitable constraints on the spatial square-integral of the wind…
Multifield models with a curved field space have already been shown to be able to provide viable quintessence models for steep potentials that satisfy swampland bounds. The simplest dynamical systems of this type are obtained by coupling…
Single-file transport, where particles diffuse in narrow channels while not overtaking each other, is a fundamental model for the tracer subdiffusion observed in confined systems, such as zeolites or carbon nanotubes. This anomalous…
The first super-convergent hybridisable discontinuous Galerkin (HDG) method for linear elastic problems capable of using the same degree of approximation for both the primal and mixed variables is presented. The key feature of the method is…
In the paper, we investigate the nonlinear thermoelasticity model in two- and three-dimensional convex and bounded domains. We propose new boundary conditions for the displacement. These conditions are not usual in thermoelasticity.…