A <scp>least‐squares</scp> finite element method based on the Helmholtz decomposition for hyperbolic balance laws
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Publication:6088402
DOI10.1002/num.22480arXiv1911.05831OpenAlexW2988049787MaRDI QIDQ6088402
Thomas A. Manteuffel, Delyan Z. Kalchev
Publication date: 14 December 2023
Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1911.05831
conservation lawsweak solutionsBurgers equationfinite element methodsHelmholtz decompositionleast-squares methodshyperbolic balance lawsspace-time discretizationnegative-norm methods
Cites Work
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- The Riemann problem of the Burgers equation with a discontinuous source term
- Implementation of the entropy viscosity method with the discontinuous Galerkin method
- Entropy viscosity method for nonlinear conservation laws
- Mathematical aspects of discontinuous Galerkin methods.
- Least-squares finite element methods
- Local error estimates and adaptive refinement for first-order system least squares (FOSLS)
- The numerical interface coupling of nonlinear hyperbolic systems of conservation laws. I: The scalar case
- High-order local maximum principle preserving (MPP) discontinuous Galerkin finite element method for the transport equation
- Scalar conservation laws with discontinuous flux function. I: The viscous profile condition
- SUPG finite element computation of compressible flows with the entropy and conservation variables formulations
- Improved Least-squares Error Estimates for Scalar Hyperbolic Problems
- A Comparative Study of Least-squares, SUPG and Galerkin Methods for Convection Problems
- A Second-Order Maximum Principle Preserving Lagrange Finite Element Technique for Nonlinear Scalar Conservation Equations
- Efficiency Based Adaptive Local Refinement for First-Order System Least-Squares Formulations
- Curvilinear finite elements for Lagrangian hydrodynamics
- Efficiency‐based h‐ and hp‐refinement strategies for finite element methods
- Finite Element Methods for Navier-Stokes Equations
- Least-squares finite elements for first-order hyperbolic systems
- Why Nonconservative Schemes Converge to Wrong Solutions: Error Analysis
- Finite Volume Methods for Hyperbolic Problems
- The Auxiliary Space Preconditioner for the de Rham Complex
- Least-Squares Finite Element Methods and Algebraic Multigrid Solvers for Linear Hyperbolic PDEs
- Mixed and least‐squares finite element methods with application to linear hyperbolic problems
- High-Order Curvilinear Finite Element Methods for Lagrangian Hydrodynamics
- Numerical Conservation Properties of H(div)-Conforming Least-Squares Finite Element Methods for the Burgers Equation
- The Mathematical Theory of Finite Element Methods
- Systems of conservation laws
- A First-Order System Least Squares Finite Element Method for the Shallow Water Equations
- Weak solutions of nonlinear hyperbolic equations and their numerical computation
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