Reliable anisotropic-adaptive discontinuous Galerkin method for simplified \(\mathbf{P}_{\mathbf{N}}\) approximations of radiative transfer

DOI10.1016/j.cam.2017.12.039zbMath1448.65230OpenAlexW2781572686MaRDI QIDQ1747310

Stefano Giani

Publication date: 4 May 2018

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2017.12.039

zbMATH Keywords

radiative transfererror estimatordiscontinuous Galerkinanisotropic adaptivity

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Radiative heat transfer (80A21)

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\(khp\)-adaptive spectral projection based discontinuous Galerkin method for the numerical solution of wave equations with memory

Uses Software

• MUMPS

Cites Work

• Unnamed Item
• A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
• An a-posteriori error estimate for \(hp\)-adaptive DG methods for convection-diffusion problems on anisotropically refined meshes
• A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
• Discontinuous Galerkin methods on \(hp\)-anisotropic meshes. I: A priori error analysis
• Discontinuous Galerkin methods on \(hp\)-anisotropic meshes. II: A posteriori error analysis and adaptivity
• A robust a-posteriori error estimator for discontinuous Galerkin methods for convection-diffusion equations
• High-order accurate discontinuous finite element solution of the 2D Euler equations
• Anisotropic error estimates for elliptic problems
• A discontinuous Galerkin method with Lagrange multipliers for the solution of Helmholtz problems in the mid-frequency regime
• Multifrontal parallel distributed symmetric and unsymmetric solvers
• An a posteriori residual error estimator for the finite element method on anisotropic tetrahedral meshes
• A note on the design of \(hp\)-adaptive finite element methods for elliptic partial differential equations
• Simplified \(P_N\) approximations to the equations of radiative heat transfer and applications
• \(h p\)-adaptive discontinuous Galerkin methods for simplified \(\operatorname{P}_{\operatorname{N}}\) approximations of frequency-dependent radiative transfer
• A Local Problem Error Estimator for Anisotropic Tetrahedral Finite Element Meshes
• A priori error estimate for the Baumann–Oden version of the discontinuous Galerkin method
• $hp$-DGFEM for Second Order Elliptic Problems in Polyhedra II: Exponential Convergence
• ENERGY NORM A POSTERIORI ERROR ESTIMATION FOR hp-ADAPTIVE DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC PROBLEMS IN THREE DIMENSIONS
• A robust a posteriori error estimate for hp-adaptive DG methods for convection-diffusion equations
• Continuous interior penalty $hp$-finite element methods for advection and advection-diffusion equations
• ENERGY NORM A POSTERIORI ERROR ESTIMATION OF hp-ADAPTIVE DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC PROBLEMS
• An Anisotropic Error Indicator Based on Zienkiewicz--Zhu Error Estimator: Application to Elliptic and Parabolic Problems
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• NUMERICAL METHODS AND OPTIMAL CONTROL FOR GLASS COOLING PROCESSES
• Discontinuous Galerkin Approximation of the Maxwell Eigenproblem