Numerical methods for fourth order nonlinear degenerate diffusion problems.

DOI10.1023/B:APOM.0000034537.55985.44zbMath1090.35086OpenAlexW2034730376MaRDI QIDQ558574

Günther Grün, Martin Rumpf, Jörg Becker, Martin O. Lenz

Publication date: 1 July 2005

Published in: Applications of Mathematics (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/33129

zbMATH Keywords

finite element methodfinite volume methodthin filmfourth order degenerate parabolic equationsurfactant driven flow

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Initial-boundary value problems for higher-order parabolic equations (35K35) Thin fluid films (76A20) Finite volume methods applied to problems in fluid mechanics (76M12) Degenerate parabolic equations (35K65) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element methods applied to problems in fluid mechanics (76M10) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

Related Items (7)

Multiscale modelling of evolving foams ⋮ Optimal control for the thin film equation: convergence of a multi-parameter approach to track state constraints avoiding degeneracies ⋮ Qualitative behaviour of solutions in two models of thin liquid films ⋮ The generalized finite volume SUSHI scheme for the discretization of the Peaceman model. ⋮ Preconditioning a class of fourth order problems by operator splitting ⋮ Numerical investigations on self-similar solutions of the nonlinear diffusion equation ⋮ When central finite differencing gives complex values for a real solution!

Cites Work

• Higher order nonlinear degenerate parabolic equations
• Finite element approximation of a fourth order nonlinear degenerate parabolic equation
• Nonnegativity preserving convergent schemes for the thin film equation
• Droplet spreading under weak slippage: The optimal asymptotic propagation rate in the multi-dimensional case.
• Nonnegative solutions of a fourth-order nonlinear degenerate parabolic equation
• Degenerate parabolic differential equations of fourth order and a plasticity model with nonlocal hardening
• Finite speed of propagation and continuity of the interface for thin viscous flows
• The thin viscous flow equation in higher space dimensions
• The finite volume method for Richards equation
• Simulation of singularities and instabilities arising in thin film flow
• On fully practical finite element approximations of degenerate Cahn-Hilliard systems
• One-Sided Difference Approximations for Nonlinear Conservation Laws
• Insoluble surfactant spreading on a thin viscous film: shock evolution and film rupture
• On a Fourth-Order Degenerate Parabolic Equation: Global Entropy Estimates, Existence, and Qualitative Behavior of Solutions
• Droplet Spreading Under Weak Slippage: A Basic Result on Finite Speed of Propagation
• Droplet spreading: Intermediate scaling law by PDE methods
• On the convergence of entropy consistent schemes for lubrication type equations in multiple space dimensions
• On the Cahn–Hilliard Equation with Degenerate Mobility
• Positivity-Preserving Numerical Schemes for Lubrication-Type Equations
• Semi-implicit finite volume scheme for solving nonlinear diffusion equations in image processing
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