相关论文: New Higher-Order Mass-Lumped Tetrahedral Elements …
We present degrees of freedom to accompany the approximation spaces already presented in a companion paper and thus complete the definition of families of high-order conforming finite elements on pyramids for the spaces of the de Rham…
We report on numerical studies of two-dimensional electron systems in the presence of a perpendicular magnetic field, with a high Landau level index (N > 1) half filled by electrons. Strong and sharp peaks are found in the wave vector…
Computational analysis with the finite element method requires geometrically accurate meshes. It is well known that high-order meshes can accurately capture curved surfaces with fewer degrees of freedom in comparison to low-order meshes.…
The purpose of this research is to describe an efficient iterative method suitable for obtaining high accuracy solutions to high frequency time-harmonic scattering problems. The method allows for both refinement of local polynomial degree…
Advancements in the synthesis of faceted nanoparticles and colloids have spurred interest in the phase behavior of polyhedral shapes. Regular tetrahedra have attracted particular attention because they prefer local symmetries that are…
A method for adaptive model order reduction for nonsmooth discrete element simulation is developed and analysed in numerical experiments. Regions of the granular media that collectively move as rigid bodies are substituted with rigid bodies…
Amorphous multi-element materials offer unprecedented tunability in composition and properties, yet their rational design remains challenging due to the lack of predictive structure-property relationships and the vast configurational space.…
This paper develops and analyzes an optimal-order semi-discrete scheme and its fully discrete finite element approximation for nonlinear stochastic elastic wave equations with multiplicative noise. A non-standard time-stepping scheme is…
The main purpose of this article is to facilitate the implementation of space-time finite element methods in four-dimensional space. In order to develop a finite element method in this setting, it is necessary to create a numerical…
This paper introduces an extension of the Morley element for approximating solutions to biharmonic equations. Traditionally limited to piecewise quadratic polynomials on triangular elements, the extension leverages weak Galerkin finite…
This paper develops novel natural superconvergence and ultraconvergence structures for the bi-$k$-order finite volume element (FVE) method on rectangular meshes. These structures furnish tunable and possibly asymmetric superconvergence and…
Different novel organic-chemical possibilities for tetrahedral building units are considered, with attention to their utility in constructing different super-structures. As a representative construction we consider the use of sets of 20…
We introduce a new class of mixed finite element methods for 2D and 3D compressible nonlinear elasticity. The independent unknowns of these conformal methods are displacement, displacement gradient, and the first Piola-Kirchhoff stress…
Given a function f defined on a bidimensional bounded domain and a positive integer N, we study the properties of the triangulation that minimizes the distance between f and its interpolation on the associated finite element space, over all…
We propose a novel Hybrid High-Order method for the Cahn-Hilliard problem with convection. The proposed method is valid in two and three space dimensions, and it supports arbitrary approximation orders on general meshes containing…
A crucial part of successful wave propagation related inverse problems is an efficient and accurate numerical scheme for solving the seismic wave equations. In particular, the numerical solution to a multi-dimensional Helmholtz equation can…
Topological materials present unconventional electronic properties that make them attractive for both basic science and next-generation technological applications. The majority of currently known topological materials have been discovered…
Finite element methods are well-known to admit robust optimal convergence on simplicial meshes satisfying the maximum angle conditions. But how to generalize this condition to polyhedra is unknown in the literature. In this work, we argue…
Millimeter-wave communication has the potential to deliver orders of magnitude increases in mobile data rates. A key design challenge is to enable rapid beam alignment with phased arrays. Traditional millimeter-wave systems require a high…
We provide, for the first time, in a doped strongly correlated system (two-leg ladder), a controlled theoretical demonstration of the existence of a state in which long-range ordered orbital currents are arranged in a staggered…