A Stabilized DG Cut Cell Method for Discretizing the Linear Transport Equation
DOI10.1137/19M1268318zbMath1469.65147arXiv1906.05642OpenAlexW3107293369MaRDI QIDQ5147964
Andreas Nüßing, Sandra May, Florian Streitbürger, Christian Engwer
Publication date: 29 January 2021
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1906.05642
stabilizationdiscontinuous Galerkin methodcut cellunfitted finite elementssmall cell problemlinear transport equation.
Hyperbolic conservation laws (35L65) 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) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) First-order hyperbolic equations (35L02)
Related Items (11)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- An unfitted discontinuous Galerkin method for pore-scale simulations of solute transport
- Ghost penalty
- Mathematical aspects of discontinuous Galerkin methods.
- A generic grid interface for parallel and adaptive scientific computing. I: Abstract framework
- A generic grid interface for parallel and adaptive scientific computing. II: Implementation and tests in DUNE
- A vertex-based hierarchical slope limiter for \(p\)-adaptive discontinuous Galerkin methods
- Optimal implicit strong stability preserving Runge-Kutta methods
- M-matrix characterizations. I: nonsingular M-matrices
- Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
- Geometrically unfitted finite element methods and applications. Proceedings of the UCL workshop, London, UK, January, 6--8, 2016
- Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid-structure interaction, and free surface flow. I
- A supraconvergent scheme for nonlinear hyperbolic systems
- Contractivity in the numerical solution of initial value problems
- An unfitted finite element method, based on Nitsche's method, for elliptic interface problems.
- An adaptive Cartesian grid method for unsteady compressible flow in irregular regions
- The aggregated unfitted finite element method for elliptic problems
- A stabilized cut discontinuous Galerkin framework for elliptic boundary value and interface problems
- A note on the stability parameter in Nitsche's method for unfitted boundary value problems
- An explicit implicit scheme for cut cells in embedded boundary meshes
- A robust CFL condition for the discontinuous Galerkin method on triangular meshes
- Higher order cut finite elements for the wave equation
- A Cartesian grid embedded boundary method for hyperbolic conservation laws
- Two-Dimensional Slope Limiters for Finite Volume Schemes on Non-Coordinate-Aligned Meshes
- A Simplified h-box Method for Embedded Boundary Grids
- CutFEM: Discretizing geometry and partial differential equations
- Riemann Solvers and Numerical Methods for Fluid Dynamics
- An unfitted finite element method using discontinuous Galerkin
- Fitted and Unfitted Finite-Element Methods for Elliptic Equations with Smooth Interfaces
- Total variation diminishing Runge-Kutta schemes
- H-Box Methods for the Approximation of Hyperbolic Conservation Laws on Irregular Grids
- Geometric Reconstruction of Implicitly Defined Surfaces and Domains with Topological Guarantees
- A high‐order discontinuous Galerkin method for compressible flows with immersed boundaries
- A High-Resolution Rotated Grid Method for Conservation Laws with Embedded Geometries
- Front tracking for hyperbolic conservation laws
This page was built for publication: A Stabilized DG Cut Cell Method for Discretizing the Linear Transport Equation