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 language | English |
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Pages (from-to) | 971-989 |
Number of pages | 19 |
Journal | Mathematics of Computation |
Volume | 68 |
Issue number | 227 |
Publication status | Published - Jul 1 1999 |
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
- Computational Mathematics
- Applied Mathematics