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Sparse grid time-discontinuous Galerkin method with streamline diffusion for transport equations
High-dimensional transport equations frequently occur in science and engineering. Computing their numerical solution, however, is challenging due to...
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A streamline-derivative-based local projection stabilization virtual element method for nonlinear convection–diffusion–reaction equation
We present a local projection stabilization for the virtual element discretization of the nonlinear convection–diffusion–reaction equation. We...
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A Hybridizable Discontinuous Galerkin Method for Magnetic Advection–Diffusion Problems
We propose and analyze a hybridizable discontinuous Galerkin (HDG) method for solving a mixed magnetic advection–diffusion problem within a more...
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Virtual element method for the quasilinear convection-diffusion-reaction equation on polygonal meshes
In this paper, we analyze the virtual element method for the quasilinear convection-diffusion-reaction equation. The most important part in the...
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Discontinuous Galerkin Method Based on the Reduced Space for the Nonlinear Convection–Diffusion–Reaction Equation
In this paper, by introducing a reconstruction operator based on the Legendre moments, we construct a reduced discontinuous Galerkin (RDG) space that...
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Consistent streamline residual-based artificial viscosity stabilization for numerical simulation of incompressible turbulent flow by isogeometric analysis
In this paper, we propose a new stabilization technique for numerical simulation of incompressible turbulent flow by solving Reynolds-averaged...
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The supercloseness of the finite element method for a singularly perturbed convection-diffusion problem on a Bakhvalov-type mesh in 2D
For singularly perturbed convection-diffusion problems, supercloseness analysis of the finite element method is still open on Bakhvalov-type meshes,...
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A weak Galerkin finite-element method for singularly perturbed convection–diffusion–reaction problems with interface
In this paper, a weak Galerkin (WG) finite-element method is developed and analyzed for singularly perturbed convection–diffusion–reaction problems...
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Multilevel Monte Carlo Methods for Stochastic Convection–Diffusion Eigenvalue Problems
We develop new multilevel Monte Carlo (MLMC) methods to estimate the expectation of the smallest eigenvalue of a stochastic convection–diffusion...
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Analysis of the local discontinuous Galerkin method with generalized fluxes for one-dimensional nonlinear convection-diffusion systems
In this paper, we present optimal error estimates of the local discontinuous Galerkin method with generalized numerical fluxes for one-dimensional...
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A Dimensional-Splitting Weak Galerkin Finite Element Method for 2D Time-Fractional Diffusion Equation
In this article, the weak Galerkin finite element method, coupled with an operator-splitting method or known as dimensional-splitting technique, is...
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Virtual Element Method for Nonlinear Time-Dependent Convection-Diffusion-Reaction Equation
In this paper, we study the numerical solution of nonlinear time dependent convection-diffusion-reaction equation using virtual element method. We...
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Bernstein-Bézier Galerkin-Characteristics Finite Element Method for Convection-Diffusion Problems
A class of Bernstein-Bézier basis based high-order finite element methods is developed for the Galerkin-characteristics solution of...
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A SUPG formulation augmented with shock-capturing for solving convection-dominated reaction–convection–diffusion equations
In this computational study, stabilized finite element solutions of convection-dominated stationary and linear reaction–convection–diffusion...
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Worked Out Problem 15: Stabilized Reduced Method for an Advection Dominated Problem
In this chapter, we consider a scalar advection-diffusion PDE modeling a stabilized advection dominated flow problem in a two-dimensional domain. The...
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An Efficient DWR-Type a Posteriori Error Bound of SDFEM for Singularly Perturbed Convection–Diffusion PDEs
This article deals with the residual-based a posteriori error estimation in the standard energy norm for the streamline-diffusion finite element...
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Non-Symmetric Interior Penalty Galerkin Finite Element Method for a Class of Singularly Perturbed Reaction Diffusion Problems with Discontinuous Data
This paper presents a non-symmetric interior penalty Galerkin finite element method for a class of one dimensional singularly perturbed...
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A stabilized finite element method for inverse problems subject to the convection–diffusion equation. II: convection-dominated regime
We consider the numerical approximation of the ill-posed data assimilation problem for stationary convection–diffusion equations and extend our...
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Global ML Stability of the Delayed Fractional-Order Coupled Reaction-Diffusion System on Networks without Strong Connectedness
This chapter primarily focuses on examining the existence of solutions and the global Mittag-Leffler stability in delayed fractional-order coupled...