Related papers: A Face-Upwinded Spectral Element Method
This article discusses a mixed FE technique for 3D nonlinear elasticity using a Hu-Washizu (HW) type variational principle. Here, the deformed configuration and sections from its cotangent bundle are taken as additional input arguments. The…
We present the marginal unbiased score expansion (MUSE) method, an algorithm for generic high-dimensional hierarchical Bayesian inference. MUSE performs approximate marginalization over arbitrary non-Gaussian latent parameter spaces,…
We present a new compatible finite element advection scheme for the compressible Euler equations. Unlike the discretisations described in Cotter and Kuzmin (2016) and Shipton et al (2018), the discretisation uses the lowest-order family of…
In this paper we analyze a space-time unfitted finite element method for the discretization of scalar surface partial differential equations on evolving surfaces. For higher order approximations of the evolving surface we use the technique…
Three algebraically stabilized finite element schemes for discretizing convection-diffusion-reaction equations are studied on adaptively refined grids. These schemes are the algebraic flux correction (AFC) scheme with Kuzmin limiter, the…
We study a higher-order surface finite element (SFEM) penalty-based discretization of the tangential surface Stokes problem. Several discrete formulations are investigated which are equivalent in the continuous setting. The impact of the…
Convection-diffusion equations arise in a variety of applications such as particle transport, electromagnetics, and magnetohydrodynamics. Simulation of the convection-dominated regime for these problems, even with high-fidelity techniques,…
In this paper, we use a unified framework introduced in [3] to study two classes of nonconforming immersed finite element (IFE) spaces with integral value degrees of freedom. The shape functions on interface elements are piecewise…
Meshless solution to differential equations using radial basis functions (RBF) is an alternative to grid based methods commonly used. Since the meshless method does not need an underlying connectivity in the form of control volumes or…
In the present work, strong approximation errors are analyzed for both the spatial semi-discretization and the spatio-temporal fully discretization of stochastic wave equations (SWEs) with cubic polynomial nonlinearities and additive…
In this article, using the weighted discrete least-squares, we propose a patch reconstruction finite element space with only one degree of freedom per element. As the approximation space, it is applied to the discontinuous Galerkin methods…
This study investigates high-order face and edge elements in finite element methods, with a focus on their geometric attributes, indexing management, and practical application. The exposition begins by a geometric decomposition of Lagrange…
This work proposes a novel finite volume paradigm, the face-centred finite volume (FCFV) method. Contrary to the popular vertex (VCFV) and cell (CCFV) centred finite volume methods, the novel FCFV defines the solution on the mesh faces…
In this paper we consider a class of unfitted finite element methods for discretization of partial differential equations on surfaces. In this class of methods known as the Trace Finite Element Method (TraceFEM), restrictions or traces of…
We propose a high order unfitted finite element method for solving timeharmonic Maxwell interface problems. The unfitted finite element method is based on a mixed formulation in the discontinuous Galerkin framework on a Cartesian mesh with…
This study presents a meshfree two-dimensional fractional-order Element-Free Galerkin (2D f-EFG) method as a viable alternative to conventional mesh-based FEM for a numerical solution of (spatial) fractional-order differential equations…
We consider the initial/boundary value problem for the fractional diffusion and diffusion-wave equations involving a Caputo fractional derivative in time. We develop two "simple" fully discrete schemes based on the Galerkin finite element…
A higher-order accurate finite element method is proposed which uses automatically generated meshes based on implicit level-set data for the description of boundaries and interfaces in two and three dimensions. The method is an alternative…
The paper studies a higher order unfitted finite element method for the Stokes system posed on a surface in three-dimensional space. The method employs generalized Taylor-Hood finite element pairs on tetrahedral bulk mesh to discretize the…
The study performs large-eddy simulations of supersonic free jet flows using the Discontinuous Galerkin Spectral Element Method (DGSEM). The main objective of the present work is to assess the resolution requirements for adequate simulation…