A new stabilized linear finite element method for solving reaction-convection-diffusion equations

DOI10.1016/j.cma.2016.04.025zbMath1439.76074OpenAlexW2206365535MaRDI QIDQ2308573

Suh-Yuh Yang, Po-Wen Hsieh

Publication date: 3 April 2020

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2016.04.025

zbMATH Keywords

boundary layerinterior layerstabilized finite element methodstabilization parameterreaction-convection-diffusion equation

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Reaction-diffusion equations (35K57) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element methods applied to problems in fluid mechanics (76M10)

Related Items (6)

A hybrid \(H^1\times H(\operatorname{curl})\) finite element formulation for a relaxed micromorphic continuum model of antiplane shear ⋮ A stabilized element-free Galerkin method for the advection-diffusion-reaction problem ⋮ HDG methods for Stokes equation based on strong symmetric stress formulations ⋮ A stable Gaussian radial basis function method for solving nonlinear unsteady convection-diffusion-reaction equations ⋮ A finite element formulation preserving symmetric and banded diffusion stiffness matrix characteristics for fractional differential equations ⋮ Convergence analysis of hybrid high-order methods for the wave equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A high-resolution Petrov-Galerkin method for the convection-diffusion-reaction problem. II: A multidimensional extension
• Analysis of the small viscosity and large reaction coefficient in the computation of the generalized Stokes problem by a novel stabilized finite element method
• Analysis of a new stabilized finite element method for the reaction-convection-diffusion equations with a large reaction coefficient
• A high-resolution Petrov-Galerkin method for the 1D convection-diffusion-reaction problem
• Finite element methods for time-dependent convection-diffusion-reaction equations with small diffusion
• On efficient least-squares finite element methods for convection-dominated problems
• Stability of semidiscrete formulations for parabolic problems at small time steps
• A new finite element formulation for computational fluid dynamics. VIII. The Galerkin/least-squares method for advective-diffusive equations
• Discontinuity-capturing finite element formulations for nonlinear convection-diffusion-reaction equations
• Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
• Stabilized finite element methods. I.: Application to the advective- diffusive model
• Stabilized finite element methods. II: The incompressible Navier-Stokes equations
• Further considerations on residual-free bubbles for advective-diffusive equations
• Bubble functions prompt unusual stabilized finite element methods.
• On an improved unusual stabilized finite element method for the advective-reactive-diffusive equation
• Revisiting stabilized finite element methods for the advective-diffusive equation
• Improving stability of stabilized and multiscale formulations in flow simulations at small time steps
• Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods
• A Novel Least-Squares Finite Element Method Enriched with Residual-Free Bubbles for Solving Convection-Dominated Problems
• On stabilized finite element methods for the Stokes problem in the small time step limit
• Steady-state convection-diffusion problems
• Finite Element Methods for Navier-Stokes Equations
• CHOOSING BUBBLES FOR ADVECTION-DIFFUSION PROBLEMS
• COMBINING ADJOINT STABILIZED METHODS FOR THE ADVECTION-DIFFUSION-REACTION PROBLEM

This page was built for publication: A new stabilized linear finite element method for solving reaction-convection-diffusion equations