Convergence of approximate solutions to an elliptic-parabolic equation without the structure condition

DOI10.1007/s00030-011-0148-8zbMath1261.35094OpenAlexW2032473903MaRDI QIDQ1928776

Petra Wittbold, Boris P. Andreianov

Publication date: 4 January 2013

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00030-011-0148-8

zbMATH Keywords

finite volume methodpenalizationelliptic-parabolic equationstructure conditionconvergence of approximate solutionsmonotone time-implicit finite volume scheme

Mathematics Subject Classification ID

Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08) Initial-boundary value problems for PDEs of mixed type (35M13) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Quasilinear parabolic equations (35K59)

Related Items (4)

Time Compactness Tools for Discretized Evolution Equations and Applications to Degenerate Parabolic PDEs ⋮ Elliptic-parabolic equation and the corresponding problem with free boundary. II: A smooth solution ⋮ On classes of well-posedness for quasilinear diffusion equations in the whole space ⋮ Elliptic-parabolic equation and the corresponding problem with free boundary. I: Elliptic problem with parameter

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Renormalized solutions of the fractional Laplace equation
• Quasilinear elliptic-parabolic differential equations
• Uniqueness of renormalized solutions of degenerate elliptic-parabolic problems
• Entropy solutions for nonlinear degenerate problems
• Convergence of a finite volume scheme for nonlinear degenerate parabolic equations
• On uniqueness techniques for degenerate convection-diffusion problems
• \(L^ 1\)-contraction and uniqueness for quasilinear elliptic-parabolic equations
• On mild and weak solutions of elliptic-parabolic problems
• Revising uniqueness for a nonlinear diffusion-convection equation
• Results concerning the nature of the continuity of solutions of parabolic equations and some of their applications
• ANALYSIS OF A FINITE VOLUME METHOD FOR A CROSS-DIFFUSION MODEL IN POPULATION DYNAMICS
• DISCRETE DUALITY FINITE VOLUME SCHEMES FOR DOUBLY NONLINEAR DEGENERATE HYPERBOLIC-PARABOLIC EQUATIONS
• Some Relations Between Nonexpansive and Order Preserving Mappings
• Sur un problème parabolique-elliptique
• Existence of renormalized solutions of degenerate elliptic-parabolic problems
• Convergence of Finite Volume Approximations for a Nonlinear Elliptic-Parabolic Problem: A "Continuous" Approach
• Uniqueness for inhomogeneous Dirichlet problem for elliptic–parabolic equations

This page was built for publication: Convergence of approximate solutions to an elliptic-parabolic equation without the structure condition