On Discrete Sobolev–Poincaré Inequalitiesfor Voronoi Finite Volume Approximations

DOI10.1007/978-3-642-20671-9_56zbMath1246.65206OpenAlexW4234951290MaRDI QIDQ2902131

Jens André Griepentrog, Annegret Glitzky

Publication date: 17 August 2012

Published in: Finite Volumes for Complex Applications VI Problems & Perspectives (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-642-20671-9_56

zbMATH Keywords

discrete Sobolev inequalitySobolev integral representationVoronoi finite volume mesh

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Finite volume methods for boundary value problems involving PDEs (65N08) Sobolev (and similar kinds of) spaces of functions of discrete variables (46E39)

Cites Work

• Energy estimates for continuous and discretized electro-reaction-diffusion systems
• Discrete Sobolev inequalities andL^perror estimates for finite volume solutions of convection diffusion equations
• Discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes SUSHI: a scheme using stabilization and hybrid interfaces
• Discrete Sobolev–Poincaré Inequalities for Voronoi Finite Volume Approximations
• Uniform exponential decay of the free energy for Voronoi finite volume discretized reaction-diffusion systems
• Exponential decay of the free energy for discretized electro-reaction–diffusion systems
• Discrete functional analysis tools for Discontinuous Galerkin methods with application to the incompressible Navier–Stokes equations
• Cell centred discretisation of non linear elliptic problems on general multidimensional polyhedral grids
• Compact embeddings of broken Sobolev spaces and applications
• Elliptic Partial Differential Equations of Second Order
• A Finite Volume Scheme for a Noncoercive Elliptic Equation with Measure Data
• Error Estimates on the Approximate Finite Volume Solution of Convection Diffusion Equations with General Boundary Conditions
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