Related papers: Multiscale Finite Element Formulations for 2D/1D P…
We analyze the flux conservation property of the finite element method. It is shown that the finite element solution does approximate the flux locally in the optimal order, i.e., the same order as that of the nodal interpolation operator.…
This paper describes in detail the implementation of a finite element technique for solving the compressible Navier-Stokes equations that is provably robust and demonstrates excellent performance on modern computer hardware. The method is…
The purpose of this work is to investigate the behavior of Multiscale Finite Element type methods for advection-diffusion problems in the advection-dominated regime. We present, study and compare various options to address the issue of the…
We develop a cut finite element method for a second order elliptic coupled bulk-surface model problem. We prove a priori estimates for the energy and $L^2$ norms of the error. Using stabilization terms we show that the resulting algebraic…
Capillary phenomena are involved in many industrial processes, especially those dealing with composite manufacturing. However, their modelling is still challenging. Therefore, a finite element setting is proposed to better investigate this…
A new numerical method is presented for solving the rotating shallow water equations on a rotating sphere using quasi-uniform polygonal meshes. The method uses special families of finite element function spaces to mimic key mathematical…
In this paper we present an advanced numerical method to simulate a real life challenging industrial problem that consists of the non-destructive testing in steam generators. We develop a finite element technique that handles the big data…
The aim of this paper is to propose an efficient adaptive finite element method for eigenvalue problems based on the multilevel correction scheme and inverse power method. This method involves solving associated boundary value problems on…
This paper is a generalization of the previous work (Yang et.al, J. Comput. Phys. 330 (2017), 863-883) to the 3-D irregular convex domains. The analytical calculation formula of fractional derivatives of finite element basis functions are…
We present a quasi-linearly scaling, first order polynomial finite element method for the solution of the magnetostatic open boundary problem by splitting the magnetic scalar potential. The potential is determined by solving a Dirichlet…
We present the mathematical theory and its numerical validation of a method tailored to include eddy-current effects only in a part of the domain. This results in a heterogeneous problem combining an eddy-current model in a subset of the…
A finite difference method (FDM) applicable to a two dimensional (2D) quantum dot was developed as a non-conventional approach to the theoretical understandings of quantum devices. This method can be applied to a realistic potential with an…
We introduce the multivariate decomposition finite element method (MDFEM) for solving elliptic PDEs with uniform random diffusion coefficients. We show that the MDFEM can be used to reduce the computational complexity of estimating the…
The aim of this work is to present the details of the finite element approach we developed for solving the Landau-Lifschitz-Gilbert equations in order to be able to treat problems involving complex geometries. There are several…
Finite-element simulations of magnetostatic fields are performed in terms of magnetic vector and total scalar potentials and compared for purpose of modeling the accelerator magnets. The potentials represent the unknown variables associated…
Elliptic interface problems whose solutions are $C^0$ continuous have been well studied over the past two decades. The well-known numerical methods include the strongly stable generalized finite element method (SGFEM) and immersed FEM…
The virtual element method (VEM) allows discretization of the problem domain with polygons in 2D. The polygons can have an arbitrary number of sides and can be concave or convex. These features, among others, are attractive for meshing…
The numerical simulation of physical processes in the underground frequently entails challenges related to the geometry and/or data. The former are mainly due to the shape of sedimentary layers and the presence of fractures and faults,…
In this paper, a symmetrized two-scale finite element method is proposed for a class of partial differential equations with symmetric solutions. With this method, the finite element approximation on a fine tensor product grid is reduced to…
A novel boundary element formulation for solving problems involving eddy currents in the thin skin depth approximation is developed. It is assumed that the time-harmonic magnetic field outside the scatterers can be described using the…