A priori Lρ error estimates for Galerkin approximations to porous medium and fast diffusion equations

Dongming Wei, Lew Lefton

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

Galerkin approximations to solutions of a Caucliy-Dirichlet problem governed by the generalized porous medium equation (formula presented) on bounded convex domains are considered. The range of the parameter ρ includes the fast diffusion case 1 <ρ <2. Using an Euler finite difference approximation in time, the semi-discrete solution is shown to converge to the exact solution in L(0, T; Lρ(Ω)) norm with an error controlled by O(Δt1/1) for 1 <p <2 and O(Δt1/2ρ) for 2 ≤ p <∞. For the fully discrete problem, a global convergence rate of O(Δt1/4) in L2(0, T; Lρ(Ω)) norm is shown for the range 2N/N+1 <ρ <2. For 2 ≤ ρ <∞, a rate of O(At1/2ρ) is shown in Lρ(0, T; Lρ(Ω)) norm.

Original languageEnglish
Pages (from-to)971-989
Number of pages19
JournalMathematics of Computation
Volume68
Issue number227
Publication statusPublished - Jul 1999
Externally publishedYes

Fingerprint

Fast Diffusion Equation
Galerkin Approximation
Porous Media
Porous materials
Error Estimates
Norm
Fast Diffusion
Porous Medium Equation
Finite Difference Approximation
Convex Domain
Generalized Equation
Global Convergence
Range of data
Dirichlet Problem
Convergence Rate
Euler
Bounded Domain
Exact Solution
Converge

Keywords

  • Cauchy-Dirichlet problem
  • Fast diffusion equation
  • Finite elements
  • Galerkin approximations
  • L error estimates
  • Porous medium equation

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics
  • Computational Mathematics

Cite this

A priori Lρ error estimates for Galerkin approximations to porous medium and fast diffusion equations. / Wei, Dongming; Lefton, Lew.

In: Mathematics of Computation, Vol. 68, No. 227, 07.1999, p. 971-989.

Research output: Contribution to journalArticle

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