Adaptive least-squares finite element methods for linear transport equations based on an H(div) flux reformulation

DOI10.1016/j.cma.2020.113041zbMath1442.65383arXiv1807.01524OpenAlexW3016664815MaRDI QIDQ2184440

Qunjie Liu, Shun Zhang

Publication date: 28 May 2020

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.01524

zbMATH Keywords

error estimatediscontinuous solutionovershootinglinear transport equationleast-squares finite element methodadaptive LSFEM

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Initial-boundary value problems for first-order hyperbolic systems (35L50)

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Cites Work

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• Handbook of numerical methods for hyperbolic problems. Basic and fundamental issues
• Mathematical aspects of discontinuous Galerkin methods.
• A class of discontinuous Petrov-Galerkin methods. I: The transport equation
• A new finite element formulation for computational fluid dynamics. VIII. The Galerkin/least-squares method for advective-diffusive equations
• Least-squares finite element methods
• Nonoscillatory solution of the steady-state inviscid Burgers' equation by mathematical programming
• Non-oscillatory and non-diffusive solution of convection problems by the iteratively reweighted least-squares finite element method
• A simple finite element method for linear hyperbolic problems
• Improved Least-squares Error Estimates for Scalar Hyperbolic Problems
• A Comparative Study of Least-squares, SUPG and Galerkin Methods for Convection Problems
• Discontinuous Finite Element Methods for Interface Problems: Robust A Priori and A Posteriori Error Estimates
• A Posteriori Error Estimation for Interior Penalty Finite Element Approximations of the Advection-Reaction Equation
• A class of discontinuous Petrov-Galerkin methods. II. Optimal test functions
• A Note on the Convergence of the Discontinuous Galerkin Method for a Scalar Hyperbolic Equation
• Least-squares finite elements for first-order hyperbolic systems
• Polynomial Approximation of Functions in Sobolev Spaces
• Multilevel Boundary Functionals for Least-Squares Mixed Finite Element Methods
• Suboptimal and Optimal Convergence in Mixed Finite Element Methods
• Least-Squares Finite Element Methods and Algebraic Multigrid Solvers for Linear Hyperbolic PDEs
• A Finite Element Technique for Solving First-Order PDEs inL^p
• DISCONTINUOUS GALERKIN METHODS FOR FIRST-ORDER HYPERBOLIC PROBLEMS
• Solution of Steady-State One-Dimensional Conservation Laws by Mathematical Programming
• Adaptive Petrov--Galerkin Methods for First Order Transport Equations
• Mixed Finite Element Methods and Applications
• Numerical Conservation Properties of H(div)-Conforming Least-Squares Finite Element Methods for the Burgers Equation
• Error Control for Discontinuous Galerkin Methods for First Order Hyperbolic Problems

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