相关论文: Shishkin mesh simulation: A new stabilization tech…
We consider variational problems that model the bending behavior of curves that are constrained to belong to given hypersurfaces. Finite element discretizations of corresponding functionals are justified rigorously via Gamma-convergence.…
We introduce a model for the mass transfer of molecular activators and inhibitors in two media separated by an interface, and study its interaction with the deformations exhibited by the two-layer skin tissue where they occur. The…
Scanning Transmission Electron Microscopy (STEM) is a critical tool for imaging the properties of materials and biological specimens at atomic scale, yet our understanding of relevant electron beam damage mechanisms is incomplete. Recent…
The local discontinuous Galerkin (LDG) method is studied for a third-order singularly perturbed problem of the convection-diffusion type. Based on a regularity assumption for the exact solution, we prove almost $O(N^{-(k+1/2)})$ (up to a…
Convection-diffusion equations provide the basis for describing heat and mass transfer phenomena as well as processes of continuum mechanics. To handle flows in porous media, the fundamental issue is to model correctly the convective…
Most recent unsupervised non-rigid 3D shape matching methods are based on the functional map framework due to its efficiency and superior performance. Nevertheless, respective methods struggle to obtain spatially smooth pointwise…
A class of different schemes for the numerical solving of semilinear singularly--perturbed reaction--diffusion boundary--value problems was constructed. The stability of the difference schemes was proved, and the existence and uniqueness of…
We address the spatial discretization of an evolution problem arising from the coupling of viscoelastic and acoustic wave propagation phenomena by employing a discontinuous Galerkin scheme on polygonal and polyhedral meshes. The coupled…
Multiscale techniques have been widely shown to potentially overcome the limitation of homogenization schemes in representing the microscopic failure mechanisms in heterogeneous media as well as their influence on their structural response…
A singularly perturbed convection-diffusion problem posed on the unit square in $\mathbb{R}^2$, whose solution has exponential boundary layers, is solved numerically using the local discontinuous Galerkin (LDG) method with piecewise…
We present two continuum models A and B to study the convective instability of granular materials subjected to vibrations. We carry out the linear stability analysis for model A and uncover the instability mechanism as a supercritical…
This paper was originally published in June 2013 in JFM (vol. 725). There was one result concerning an expression of viscous dissipation in convective flows and a second result on the condition of applicability of the anelastic liquid…
This work presents a detailed mathematical model combined with an innovative efficient numerical model to predict heat, air and moisture transfer through porous building materials. The model considers the transient effects of air transport…
We present recent finite element numerical results on a model convection-diffusion problem in the singular perturbed case when the convection term dominates the problem. We compare the standard Galerkin discretization using the linear…
This paper describes the generation of initial conditions for numerical simulations in cosmology with multiple levels of resolution, or multiscale simulations. We present the theory of adaptive mesh refinement of Gaussian random fields…
In this article we consider the numerical approximation of the convection-diffusion-reaction equation. One of the main challenges of designing a numerical method for this problem is that boundary layers occurring in the convection-dominated…
The first paper of this series [J. Chem. Phys. 158, 034103 (2023)] demonstrated that excess entropy scaling holds for both fine-grained and corresponding coarse-grained (CG) systems. Despite its universality, a more exact determination of…
In this work, we investigate a numerical procedure for recovering a space-dependent diffusion coefficient in a (sub)diffusion model from the given terminal data, and provide a rigorous numerical analysis of the procedure. By exploiting…
Algebraically stabilized finite element discretizations of scalar steady-state convection-diffusion-reaction equations often provide accurate approximate solutions satisfying the discrete maximum principle (DMP). However, it was observed…
We present an adaptive simulation framework for binary-fluid flows, based on the Abels-Garcke-Gr\"un Navier-Stokes-Cahn-Hilliard (AGG NSCH) diffuse-interface model. The adaptive-refinement procedure is guided by a two-level hierarchical…