The effect of the consistent mass matrix on the maximum-principle for scalar conservation equations

DOI10.1007/s10915-016-0285-7zbMath1368.65192OpenAlexW2519443806MaRDI QIDQ2356616

Yong Yang, Bojan Popov, Jean-Luc Guermond

Publication date: 6 June 2017

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-016-0285-7

zbMATH Keywords

maximum principlefinite element methodweak formulationCauchy problemperiodic boundary value problemmass lumpingconsistent mass matrixnonlinear conservation equation

Mathematics Subject Classification ID

Maximum principles in context of PDEs (35B50) Hyperbolic conservation laws (35L65) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

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Cites Work

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• A maximum-principle preserving \(C^0\) finite element method for scalar conservation equations
• A correction technique for the dispersive effects of mass lumping for transport problems
• Non-oscillatory central differencing for hyperbolic conservation laws
• Towards the ultimate conservative difference scheme. II: Monotonicity and conservation combined in a second-order scheme
• Flux correction tools for finite elements
• On nonlinear artificial viscosity, discrete maximum principle and hyperbolic conservation laws
• Maximum-principle-satisfying and positivity-preserving high-order schemes for conservation laws: survey and new developments
• Maximum principle and convergence of central schemes based on slope limiters
• Generalized Fourier analyses of the advection–diffusion equation—Part I: one-dimensional domains
• Invariant Domains and First-Order Continuous Finite Element Approximation for Hyperbolic Systems
• Riemann Solvers, the Entropy Condition, and Difference
• Flux-Corrected Transport
• Positive schemes and shock modelling for compressible flows
• On Monotonicity-Preserving Stabilized Finite Element Approximations of Transport Problems
• Stabilized Galerkin approximation of convection-diffusion-reaction equations: discrete maximum principle and convergence
• On the existence of maximum principles in parabolic finite element equations
• Weak solutions of nonlinear hyperbolic equations and their numerical computation

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