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A multipoint flux mixed finite element method with mass-conservative characteristic finite element method for incompressible miscible displacement problem
In this paper, we consider a decoupled and mass-conservative numerical scheme for the incompressible miscible displacement problem in porous media by...
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Operator-splitting finite element method for solving the radiative transfer equation
An operator-splitting finite element scheme for the time-dependent radiative transfer equation is presented in this paper. The streamline upwind...
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Moving mesh method with variational multiscale finite element method for convection–diffusion–reaction equations
The solutions tend to have large gradients, discontinuities, or sharp layers for convection-dominated convection–diffusion–reaction equations. Many...
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An MP-DWR method for h-adaptive finite element methods
In a dual-weighted residual method based on the finite element framework, the Galerkin orthogonality is an issue that prevents solving the dual...
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The development of an ALE finite element and discontinuous Galerkin method for the non-isothermal non-Newtonian FSI problem
In this paper, we develop a semi-implicit partitioned finite element and discontinuous Galerkin method for the non-isothermal non-Newtonian fluid...
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A cell-based smoothed finite-element method for gradient elasticity
In this paper, the cell-based smoothed finite-element method (CS-FEM) is proposed for solving boundary value problems of gradient elasticity in two...
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Cut-PFEM: a Particle Finite Element Method using unfitted boundary meshes
In this work, we present a novel unfitted mesh boundary strategy in the context of the Particle Finite Flement Method (PFEM) aiming to improve...
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Data-driven multiscale finite-element method using deep neural network combined with proper orthogonal decomposition
In this paper, a data-driven multiscale finite-element method (data-driven FE 2 ) is proposed using a deep neural network (DNN) and proper orthogonal...
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A parallel two-grid method based on finite element approximations for the 2D/3D Navier–Stokes equations with dam**
Based on two-grid discretizations, this paper introduces a parallel finite element method for the 2D/3D Navier–Stokes equations with dam**. In this...
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Optimal error estimates of penalty difference finite element method for the 3D steady Navier-Stokes equations
In this paper, a penalty difference finite element (PDFE) method is presented for the 3D steady Navier-Stokes equations by using the finite element...
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An alternating direction implicit finite element Galerkin method for the linear Schrödinger equation
We formulate and analyze a fully discrete approximate solution of the linear Schrödinger equation on the unit square written as a Schrödinger-type...
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Supercloseness and postprocessing for linear finite element method on Bakhvalov-type meshes
Supercloseness and postprocessing of the linear finite element method are studied on the Bakhvalov-type mesh for a singularly perturbed convection...
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A novel enriched degree of freedom method for absorbing boundary conditions in the time-domain finite element method
This paper proposes an enriched degree of freedom method for absorbing boundary conditions in the time-domain finite element method (TD-FEM). In the...
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Coupled hydro-mechanical two-phase flow model in fractured porous medium with the combined finite-discrete element method
This paper presents a time-explicit, fully coupled, hydro-mechanical model to simulate the two-phase flow process in fractured porous media,...
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Surrogate modeling for interactive tunnel track design using the cut finite element method
The Cut Finite Element Method (CutFEM) is recently shown to be a versatile approach for tunnel construction modeling and settlement analysis. The...
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A weak Galerkin finite element method for singularly perturbed problems with two small parameters on Bakhvalov-type meshes
A weak Galerkin finite element method is proposed and analyzed for solving two-parameter singularly perturbed differential equations on...
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A new expanded mixed finite element method for Kirchhoff type parabolic equation
A new expanded mixed finite element method is constructed for solving the Kirchhoff type parabolic equation. Compared with the traditional mixed...
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An ANN-assisted efficient enriched finite element method via the selective enrichment of moment fitting
Enrichment techniques that employ nonconforming mesh are effective in modeling structures with discontinuities because numerical issues regarding...
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Uniform convergence of optimal order for a finite element method on a Bakhvalov-type mesh for a singularly perturbed convection-diffusion equation with parabolic layers
This paper is to analyze a finite element method of any order on a Bakhvalov-type mesh in the case of 2D. By introducing a new interpolation...
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Unconditionally convergent and superconvergent finite element method for nonlinear time-fractional parabolic equations with distributed delay
In this paper, we propose an efficient Newton linearized numerical method for the nonlinear time-fractional parabolic equations with distributed...
