High order ADER-IPDG methods for the unsteady advection-diffusion equation
DOI10.1007/s42967-023-00355-wMaRDI QIDQ6593786
Michel Bergmann, Alexis Tardieu, Afaf Bouharguane, Angelo Iollo
Publication date: 27 August 2024
Published in: Communications on Applied Mathematics and Computation (Search for Journal in Brave)
advection-diffusionhigh-order schemesGalerkinempirical convergence ratesarbitrary high order derivatives (ADER) approachinterior penalty discontinuous Galerkin (IPDG)
Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)
Cites Work
- Explicit one-step time discretizations for discontinuous Galerkin and finite volume schemes based on local predictors
- ADER schemes for nonlinear systems of stiff advection-diffusion-reaction equations
- Central ADER schemes for hyperbolic conservation laws
- A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes
- Explicit Runge-Kutta residual distribution schemes for time dependent problems: second order case
- Residual distribution schemes: current status and future trends
- Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
- ADER: Arbitrary high-order Godunov approach
- Design and analysis of ADER-type schemes for model advection-diffusion-reaction equations
- Arbitrary-Lagrangian-Eulerian discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes
- On high order ADER discontinuous Galerkin schemes for first order hyperbolic reformulations of nonlinear dispersive systems
- An Eulerian finite-volume approach of fluid-structure interaction problems on quadtree meshes
- ADER scheme for incompressible Navier-Stokes equations on overset grids with a compact transmission condition
- Efficient implementation of ADER discontinuous Galerkin schemes for a scalable hyperbolic PDE engine
- Semi-implicit discontinuous Galerkin methods for the incompressible Navier-Stokes equations on adaptive staggered Cartesian grids
- Building blocks for arbitrary high order discontinuous Galerkin schemes
- Advection-Diffusion-Reaction Equations: Hyperbolization and High-Order ADER Discretizations
- Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations
- Discontinuous Galerkin methods
- Second Order ADER Scheme for Unsteady Advection-Diffusion on Moving Overset Grids with a Compact Transmission Condition
- The Direct Discontinuous Galerkin (DDG) Methods for Diffusion Problems
- A New Family of High Order Unstructured MOOD and ADER Finite Volume Schemes for Multidimensional Systems of Hyperbolic Conservation Laws
- High Order Accurate Direct Arbitrary-Lagrangian-Eulerian ADER-MOOD Finite Volume Schemes for Non-Conservative Hyperbolic Systems with Stiff Source Terms
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