A priori 𝐿^{𝜌} error estimates for Galerkin approximations to porous medium and fast diffusion equations

DOI10.1090/S0025-5718-99-01021-2zbMath0915.76057OpenAlexW2091275824MaRDI QIDQ4240575

Dongming Wei, Lew E. Lefton

Publication date: 28 April 1999

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-99-01021-2

zbMATH Keywords

Cauchy-Dirichlet problembounded convex domainsglobal convergence rategeneralized porous medium equationsemi-discrete solutionEuler finite difference approximation in time

Mathematics Subject Classification ID

Flows in porous media; filtration; seepage (76S05) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (7)

Finite volume element approximation for nonlinear diffusion problems with degenerate diffusion coefficients ⋮ On the diffusive wave approximation of the shallow water equations ⋮ Anisotropic mesh adaptation for finite element solution of anisotropic porous medium equation ⋮ Discrete solutions for the porous medium equation with absorption and variable exponents ⋮ A study on moving mesh finite element solution of the porous medium equation ⋮ Penalty finite element approximations of the stationary power-law Stokes problem ⋮ Bound preserving and energy dissipative schemes for porous medium equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Degenerate parabolic equations
• Finite element method for solving nonlinear parabolic systems
• Nonlinear parabolic equations involving measures as initial conditions
• Semi-discretization in time of a fast diffusion equation
• Finite element methods (Part 1)
• Uniqueness of solutions of the initial-value problem for \(u_t- \Delta\varphi (u)=0\)
• On solutions of some doubly nonlinear degenerate parabolic equations with absorption
• Sur la résolution et l'approximation de certaines équations paraboliques non linéaires dégénérées
• Sur la résolution de certaines équations paraboliques non linéaires
• Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
• Numerical Methods for Flows Through Porous Media. I
• Optimal error estimates for an approximation of degenerate parabolic problems
• Error Analysis of the Enthalpy Method for the Stefan Problem
• Some problems of the qualitative theory of non-linear degenerate second-order parabolic equations
• Approximation of Degenerate Parabolic Problems Using Numerical Integration
• Error estimates for multidimensional singular parabolic problems
• Polynomial Approximation of Functions in Sobolev Spaces
• Error Estimates for a Nonlinear Degenerate Parabolic Problem
• Improved error estimates for mixed finite‐element approximations for nonlinear parabolic equations: The discrete‐time case
• Self-similar behaviour for the equation of fast nonlinear diffusion
• Error Estimates for the Multidimensional Two-Phase Stefan Problem
• Optimal Rates of Convergence for Degenerate Parabolic Problems in Two Dimensions
• Error Analysis for Implicit Approximations to Solutions to Cauchy Problems

This page was built for publication: A priori 𝐿^{𝜌} error estimates for Galerkin approximations to porous medium and fast diffusion equations