Goal-oriented anisotropic \(hp\)-adaptive discontinuous Galerkin method for the Euler equations
DOI10.1007/s42967-020-00102-5zbMath1499.65654arXiv2007.06840OpenAlexW3159919811MaRDI QIDQ2124051
Publication date: 14 April 2022
Published in: Communications on Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2007.06840
Euler equationsdiscontinuous Galerkin methodadjoint consistencytarget functionalanisotropic \(hp\)-mesh adaptation
Transonic flows (76H05) Gas dynamics (general theory) (76N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element methods applied to problems in fluid mechanics (76M10) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Euler equations (35Q31)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Output-based space-time mesh adaptation for the compressible Navier-Stokes equations
- Adjoint-based anisotropic \(hp\)-adaptation for discontinuous Galerkin methods using a continuous mesh model
- On a robust discontinuous Galerkin technique for the solution of compressible flow
- Fully anisotropic goal-oriented mesh adaptation for 3D steady Euler equations
- Transonic flow simulations using an upstream centered scheme of Godunov in finite elements
- High-order accurate discontinuous finite element solution of the 2D Euler equations
- Grid adaptation for functional outputs: application to two-dimensional inviscid flows
- Residual based error estimates for the space-time discontinuous Galerkin method applied to the compressible flows
- Adjoint-based \textit{hp}-adaptivity on anisotropic meshes for high-order compressible flow simulations
- Goal-oriented error estimates including algebraic errors in discontinuous Galerkin discretizations of linear boundary value problems.
- Adaptive discontinuous Galerkin finite element methods for the compressible Euler equations.
- Anisotropic grid adaptation for functional outputs: application to two-dimensional viscous flows.
- A semi-implicit discontinuous Galerkin finite element method for the numerical solution of inviscid compressible flow
- A goal-oriented anisotropic \(hp\)-mesh adaptation method for linear convection-diffusion-reaction problems
- Generalized adjoint consistent treatment of wall boundary conditions for compressible flows
- An optimization-based framework for anisotropic simplex mesh adaptation
- Anisotropic \(hp\)-adaptive method based on interpolation error estimates in the \(L^q\)-norm
- Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality
- An optimal control approach to a posteriori error estimation in finite element methods
- Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems on Anisotropically Refined Meshes
- Numerical evaluation of two discontinuous Galerkin methods for the compressible Navier–Stokes equations
- A design of residual error estimates for a high order BDF‐DGFE method applied to compressible flows
- A Goal-Oriented High-Order Anisotropic Mesh Adaptation Using Discontinuous Galerkin Method for Linear Convection-Diffusion-Reaction Problems
- Discontinuous Galerkin Method
- The Role of the Jacobian in the Adaptive Discontinuous Galerkin Method for the Compressible Euler Equations
- Adjoint Consistency Analysis of Discontinuous Galerkin Discretizations
- Anisotropic mesh refinement for discontinuous Galerkin methods in two‐dimensional aerodynamic flow simulations
- On the Error of Linear Interpolation and the Orientation, Aspect Ratio, and Internal Angles of a Triangle
