相关论文: WAVEx: Stabilized Finite Elements for Spectral Win…
The electroporoelasticity model, which couples Maxwell's equations with Biot's equations, plays a critical role in applications such as water conservancy exploration, earthquake early warning, and various other fields. This work focuses on…
This paper presents a simplified weak Galerkin (WG) finite element method for solving biharmonic equations avoiding the use of traditional stabilizers. The proposed WG method supports both convex and non-convex polytopal elements in finite…
This paper presents a computational framework for modeling wave propagation in geometrically linear elastic materials characterized by algebraically nonlinear constitutive relations. We derive a specific form of the nonlinear wave equation…
A family of implicit-in-time mixed finite element schemes is presented for the numerical approximation of the acoustic wave equation. The mixed space discretization is based on the displacement form of the wave equation and the…
This paper analyzes a space-time finite element method for fractional wave problems. The method uses a Petrov-Galerkin type time-stepping scheme to discretize the time fractional derivative of order $ \gamma $ ($1<\gamma<2$). We establish…
Waves are all around us--be it in the form of sound, electromagnetic radiation, water waves, or earthquakes. Their study is an important basic tool across engineering and science disciplines. Every wave solver serving the computational…
The objective of this contribution is to develop a convergence analysis for SUPG-stabilized Virtual Element Methods in diffusion-convection problems that is robust also in the convection dominated regime. For the original method introduced…
A recently developed Eulerian finite element method is applied to solve advection-diffusion equations posed on hypersurfaces. When transport processes on a surface dominate over diffusion, finite element methods tend to be unstable unless…
This paper develops and analyzes a class of semi-discrete and fully discrete weak Galerkin finite element methods for unsteady incompressible convective Brinkman-Forchheimer equations. For the spatial discretization, the methods adopt the…
Finite element methods provide accurate and efficient methods for the numerical solution of partial differential equations by means of restricting variational problems to finite-dimensional approximating spaces. However, they do not…
The recent statistical finite element method (statFEM) provides a coherent statistical framework to synthesise finite element models with observed data. Through embedding uncertainty inside of the governing equations, finite element…
The Scaled Boundary Finite Element Method is a novel semi-analytical method jointly developed by Chongmin Song and John P Wolf to solve problems in elastodynamics and allied problems in civil engineering. This novel method has been recently…
The computational modeling of many engineering problems using the Finite Element method involves the modeling of two or more bodies that meet through an interface. The interface can be physical, as in multi-physics and contact problems, or…
We study continuous finite element dicretizations for one dimensional hyperbolic partial differential equations. The main contribution of the paper is to provide a fully discrete spectral analysis, which is used to suggest optimal values of…
Accurate dynamic modeling of power systems is essential to assess the stability of electrical power systems when faced with disturbances, which can trigger cascading failures leading to blackouts. A continuum model proves to be effective in…
This paper is concerned with mixed finite element method (FEM) for solving the two-dimensional, nonlinear fourth-order active fluid equations. By introducing an auxiliary variable $w=-\Delta u$, the original fourth problem is transformed…
We evaluate the influence of local resolution, eddy viscosity, coastline structure, and boundary conditions on the numerical representation of boundary currents in a finite element shallow-water model. The use of finite element…
This paper proposes and analyzes a class of weak Galerkin (WG) finite element methods for stationary natural convection problems in two and three dimensions. We use piecewise polynomials of degrees k, k-1, and k(k>=1) for the velocity,…
We propose a new method for spatio-temporal forecasting on arbitrarily distributed points. Assuming that the observed system follows an unknown partial differential equation, we derive a continuous-time model for the dynamics of the data…
An operator-splitting finite element scheme for the time-dependent, high-dimensional radiative transfer equation is presented in this paper. The streamline upwind Petrov-Galerkin finite element method and discontinuous Galerkin finite…