Analysis of a Combined CG1-DG2 Method for the Transport Equation

DOI10.1137/13093683XzbMath1312.65183MaRDI QIDQ5253551

Melanie Bittl, Dmitri Kuzmin, Roland Becker

Publication date: 27 May 2015

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

zbMATH Keywords

finite element discretizationa priori error estimatesconvective transportreduced discontinuous Galerkin method

Mathematics Subject Classification ID

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, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

Related Items (4)

Analysis of a family of continuous-discontinuous Galerkin FEM for convection-diffusion problems ⋮ Locally bound-preserving enriched Galerkin methods for the linear advection equation ⋮ The CG1-DG2 method for convection-diffusion equations in 2D ⋮ A new nonconforming finite element method for convection dominated diffusion-reaction equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Finite element methods for linear hyperbolic problems
• Mathematical aspects of discontinuous Galerkin methods.
• Finite element methods for time-dependent convection-diffusion-reaction equations with small diffusion
• Edge stabilization for Galerkin approximations of convection-diffusion-reaction problems
• Hierarchical slope limiting in explicit and implicit discontinuous Galerkin methods
• A vertex-based hierarchical slope limiter for \(p\)-adaptive discontinuous Galerkin methods
• Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
• A relationship between stabilized finite element methods and the Galerkin method with bubble functions
• Further considerations on residual-free bubbles for advective-diffusive equations
• A discontinuous \(hp\) finite element method for convection-diffusion problems
• \(b=\int g\)
• Flux correction tools for finite elements
• Theory and practice of finite elements.
• A discontinuous \(hp\) finite element method for diffusion problems: 1-D analysis
• Revisiting stabilized finite element methods for the advective-diffusive equation
• A multiscale discontinuous Galerkin method with the computational structure of a continuous Galerkin method
• New shape functions for triangular \(p\)-FEM using integrated Jacobi polynomials
• Implicit-explicit Runge–Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations
• A Note on the Convergence of the Discontinuous Galerkin Method for a Scalar Hyperbolic Equation
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems
• An Interior Penalty Finite Element Method with Discontinuous Elements
• A Priori Error Analysis of Residual-Free Bubbles for Advection-Diffusion Problems
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• Discontinuoushp-Finite Element Methods for Advection-Diffusion-Reaction Problems
• DISCONTINUOUS GALERKIN METHODS FOR FIRST-ORDER HYPERBOLIC PROBLEMS
• An Analysis of the Discontinuous Galerkin Method for a Scalar Hyperbolic Equation
• High-Resolution Conservative Algorithms for Advection in Incompressible Flow
• The Mathematical Theory of Finite Element Methods
• How accurate is the streamline diffusion finite element method?

This page was built for publication: Analysis of a Combined CG1-DG2 Method for the Transport Equation