A discontinuous Galerkin method by patch reconstruction for convection-diffusion-reaction problems over polytopic meshes
DOI10.1016/j.camwa.2021.05.035OpenAlexW3172558878MaRDI QIDQ2047573
Publication date: 20 August 2021
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2012.13532
boundary layersoptimal error estimatesdiscontinuous Galerkin methodsconvection-dominated regimepatch reconstructionpolytopic meshes
Boundary value problems for second-order elliptic equations (35J25) 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)
Uses Software
Cites Work
- Unnamed Item
- \texttt{PolyMesher}: a general-purpose mesh generator for polygonal elements written in Matlab
- Continuous piecewise linear finite elements for the Kirchhoff-Love plate equation
- An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators
- A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
- A robust WG finite element method for convection-diffusion-reaction equations
- An implicit high-order hybridizable discontinuous Galerkin method for linear convection-diffusion equations
- A discontinuous \(hp\) finite element method for convection-diffusion problems
- A variational multiscale interpolating element-free Galerkin method for convection-diffusion and Stokes problems
- A high order discontinuous Galerkin method with skeletal multipliers for convection-diffusion-reaction problems
- A least squares method for linear elasticity using a patch reconstructed space
- An arbitrary-order discontinuous Galerkin method with one unknown per element
- A hybrid discontinuous Galerkin method for advection-diffusion-reaction problems
- Stabilization mechanisms in discontinuous Galerkin finite element methods
- A finite element method by patch reconstruction for the Stokes problem using mixed formulations
- The mimetic finite difference method for elliptic problems
- Virtual Element Method for general second-order elliptic problems on polygonal meshes
- hp-Version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes
- $hp$-Version Composite Discontinuous Galerkin Methods for Elliptic Problems on Complicated Domains
- An Efficient High Order Heterogeneous Multiscale Method for Elliptic Problems
- A Hybridizable Discontinuous Galerkin Method for Steady-State Convection-Diffusion-Reaction Problems
- Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations
- Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems
- Mimetic finite differences for elliptic problems
- An Interior Penalty Finite Element Method with Discontinuous Elements
- The Finite Element Method with Penalty
- An Elliptic Collocation-Finite Element Method with Interior Penalties
- The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
- Poincaré--Friedrichs Inequalities for Piecewise H1 Functions
- Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
- Discontinuoushp-Finite Element Methods for Advection-Diffusion-Reaction Problems
- Recovered finite element methods on polygonal and polyhedral meshes
- A Discontinuous Galerkin Method by Patch Reconstruction for Biharmonic Problem
- hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes
- Nonconforming Elements in the Finite Element Method with Penalty
- A Weak Galerkin Finite Element Method for Singularly Perturbed Convection-Diffusion--Reaction Problems
- Stabilised \(hp\)-finite element approximation of partial differential equations with nonnegative characteristic form