相关论文: Simple finite elements and multigrid for efficient…
We develop a mixed finite element domain decomposition method on non-matching grids for the Biot system of poroelasticity. A displacement-pressure vector mortar function is introduced on the interfaces and utilized as a Lagrange multiplier…
We develop a new multipoint stress mixed finite element method for linear elasticity with weakly enforced stress symmetry on simplicial grids. Motivated by the multipoint flux mixed finite element method for Darcy flow, the method utilizes…
The numerical solution of a nonlinear and space-fractional anti-diffusive equation used to model dune morphodynamics is considered. Spatial discretization is effected using a finite element method whereas the Crank-Nicolson scheme is used…
We consider a randomised implementation of the finite element method (FEM) for elliptic partial differential equations on high-dimensional models. This is motivated by applications where model predictions are essential for real-time process…
The Kohn-Sham equation is a powerful, widely used approach for computation of ground state electronic energies and densities in chemistry, materials science, biology, and nanosciences. In this paper, we study the adaptive finite element…
The paper develops a finite element method for partial differential equations posed on hypersurfaces in $\mathbb{R}^N$, $N=2,3$. The method uses traces of bulk finite element functions on a surface embedded in a volumetric domain. The bulk…
We shall establish the convergence of an adaptive conforming finite element method for the reconstruction of the distributed flux in a diffusion system. The adaptive method is based on a posteriori error estimators for the distributed flux,…
In this paper, a direct finite element method is proposed for solving interface problems on unfitted meshes. This new method treats the two interface conditions as an $H^{\frac12}(\Gamma)\times H^{-\frac12}(\Gamma)$ pair for the mutual…
In this work, we present an efficient numerical implementation of the finite element method for modal analysis that leverages various symmetry operations, including spatial symmetry in point groups and space-time symmetry in…
This work presents an Iterative Constraint Energy Minimizing Generalized Multiscale Finite Element Method (ICEM-GMsFEM) for solving the contact problem with high contrast coefficients. The model problem can be characterized by a variational…
A method for performing high order mesh refinement multigrid computations is presented. The Full Approximation Scheme (FAS) multigrid technique is utilized for a sequence of nested patches of increasing resolution. Conservation forms are…
We propose a novel finite element method scheme for singularly perturbed advection-diffusion-reaction problems, which combines certain quantum-assisted stabilization scheme with a classical h-adaptive approach to provide automatic error…
We study mixed finite element methods for the linearized rotating shallow water equations with linear drag and forcing terms. By means of a strong energy estimate for an equivalent second-order formulation for the linearized momentum, we…
We develop an energy-decreasing algorithm for the finite element approximation of two-dimensional ferronematic equilibrium states. The problem is formulated as the minimization of the harmonic energy of two two-dimensional vector fields,…
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…
We present a numerically efficient and accurate Multiple Scattering formalism, which is a generalization of the Multiple Scattering method with a truncated basis set [X. -G. Zhang and W. H. Butler, Phys. Rev. B 46,7433 (1992)]. Compared to…
Finite differences, finite elements, and their generalizations are widely used for solving partial differential equations, and their high-order variants have respective advantages and disadvantages. Traditionally, these methods are treated…
A wildland fire model based on semi-empirical relations for the spread rate of a surface fire and post-frontal heat release is coupled with the Weather Research and Forecasting atmospheric model (WRF). The propagation of the fire front is…
In this paper, we propose offline and online adaptive enrichment algorithms for the generalized multiscale approximation of a mixed finite element method with velocity elimination to solve the subsurface flow problem in high-contrast and…
We consider the numerical approximation of compressible flow in a pipe network. Appropriate coupling conditions are formulated that allow us to derive a variational characterization of solutions and to prove global balance laws for the…