An optimization-based framework for anisotropic \(hp\)-adaptation of high-order discretizations

DOI10.1016/j.jcp.2018.09.005zbMath1416.76125OpenAlexW2890289996WikidataQ129324407 ScholiaQ129324407MaRDI QIDQ2002274

Yanyan Li

Publication date: 11 July 2019

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2018.09.005

zbMATH Keywords

high-order methods\(hp\)-mesh optimizationadjoint-based error estimatesanisotropic \(hp\)-adaptationcontinuous mesh representation

Mathematics Subject Classification ID

Gas dynamics (general theory) (76N15) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (5)

A continuous \textit{hp}-mesh model for discontinuous Petrov-Galerkin finite element schemes with optimal test functions ⋮ An anisotropic \textit{hp}-mesh adaptation method for time-dependent problems based on interpolation error control ⋮ Output-based adaptive aerodynamic simulations using convolutional neural networks ⋮ An anisotropic \(h\)-adaptive strategy for discontinuous Petrov-Galerkin schemes using a continuous mesh model ⋮ Anisotropic mesh generation and adaptation for quads using the \(L_p\)-CVT method

Uses Software

• bamg

Cites Work

• Adjoint error estimation and grid adaptation for functional outputs: Application to quasi-one-dimensional flow
• Adjoint-based \textit{hp}-adaptivity on anisotropic meshes for high-order compressible flow simulations
• A note on the design of \(hp\)-adaptive finite element methods for elliptic partial differential equations
• Fully automatic \(hp\)-adaptivity in three dimensions
• An optimization-based framework for anisotropic simplex mesh adaptation
• Energy stable flux reconstruction schemes for advection-diffusion problems
• Anisotropic \(hp\)-adaptive method based on interpolation error estimates in the \(L^q\)-norm
• Continuous Mesh Framework Part I: Well-Posed Continuous Interpolation Error
• Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• Adjoint Recovery of Superconvergent Functionals from PDE Approximations
• High‐order CFD methods: current status and perspective
• Discontinuous Galerkin Method for Time-Dependent Problems: Survey and Recent Developments
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