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Adaptive discontinuous Galerkin finite element methods for the Allen-Cahn equation on polygonal meshes
In this paper, we develop a polygonal mesh adaptation algorithm for a fully implicit scheme based on discontinuous Galerkin (DG) finite element...
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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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Optimal convergence analysis of weak Galerkin finite element methods for parabolic equations with lower regularity
This paper is devoted to investigating the optimal convergence order of a weak Galerkin finite element approximation to a second-order parabolic...
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A two-grid combined mixed finite element and discontinuous Galerkin method for a compressible miscible displacement problem
A compressible miscible displacement problem is modeled by a nonlinear coupled system with partial differential equations in porous media. A two-grid...
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A comparative study on interior penalty discontinuous Galerkin and enriched Galerkin methods for time-fractional Sobolev equation
This study documents the development of a novel scheme for spatial discretization of the time-fractional Sobolev equation. The scheme is based on a...
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A weak Galerkin pseudostress-based mixed finite element method on polygonal meshes: application to the Brinkman problem appearing in porous media
In this paper, we extend the utilization of pseudostress-based formulation, recently employed for solving diverse linear and nonlinear problems in...
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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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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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Mixed Finite Element Methods for the Navier–Stokes–Biot Model
We present two mixed finite element methods for the quasistatic Navier–Stokes–Biot model. The methods are based on a fully-mixed formulation, using...
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A priori error estimates of a discontinuous Galerkin method for the Navier-Stokes equations
This-36pt paper considers a discontinuous Galerkin finite element method for the 2 D transient and incompressible Navier-Stokes model. Following the...
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An interior penalty discontinuous Galerkin reduced order model for the variable coefficient advection–diffusion-reaction equation
In this paper, we construct a reduced order model (ROM) to solve the advection–diffusion-reaction (ADR) equation with variable coefficients. In order...
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Superconvergence error estimates of discontinuous Galerkin time step** for singularly perturbed parabolic problems
A parabolic convection-diffusion-reaction problem is discretized by the non-symmetric interior penalty Galerkin (NIPG) method in space and...
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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 local discontinuous Galerkin method for multi-dimensional linear convection-diffusion equations
We construct and analyze a local discontinuous Galerkin (LDG) method which is combined with the locally one-dimensional method as one of the...
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Machine learning mesh-adaptation for laminar and turbulent flows: applications to high-order discontinuous Galerkin solvers
We present a machine learning-based mesh refinement technique for steady and unsteady incompressible flows. The clustering technique proposed by...
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A superconvergent ultra-weak local discontinuous Galerkin method for nonlinear fourth-order boundary-value problems
In this paper, we focus on constructing and analyzing a superconvergent ultra-weak local discontinuous Galerkin (UWLDG) method for the...
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A posteriori error analysis of an ultra-weak local discontinuous Galerkin method for nonlinear fourth-order boundary-value problems
In this paper, we present and analyze a posteriori error estimates for the ultra-weak local discontinuous Galerkin (UWLDG) method applied to...
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Balanced-norm error estimate of the local discontinuous Galerkin method on layer-adapted meshes for reaction-diffusion problems
We study the local discontinuous Galerkin (LDG) method on layer-adapted meshes for singularly perturbed problems. For these problems of...
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Element-free Galerkin analysis of MHD duct flow problems at arbitrary and high Hartmann numbers
A stabilized element-free Galerkin (EFG) method is proposed in this paper for numerical analysis of the generalized steady MHD duct flow problems at...
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Parallel Non-Conforming Finite Element Technique for Mathematical Simulation of Fluid Flow in Multiscale Porous Media
We consider the three-dimensional steady-state incompressible fluid flow problem in a heterogeneous porous medium using the framework of the...