Finite Element Approximation of the Transport of Reactive Solutes in Porous Media. Part 1: Error Estimates for Nonequilibrium Adsorption Processes
Barrett JW, Knabner P (1997)
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 1997
Journal
Publisher: Society for Industrial and Applied Mathematics
Book Volume: 34
Pages Range: 201-227
Journal Issue: 1
DOI: 10.1137/S0036142993249024
Abstract
In this paper we analyze a fully practical piecewise linear finite element approximation involving numerical integration, backward Euler time discretization, and possibly regularization of the following degenerate parabolic system arising in a model of reactive solute transport in porous media: find {u(x, t),v(x,t)} such that ∂u + ∂v- δu = f in ω × (0,T] u = 0 on ∂ω × (0,T] ∂v = k((℘(u) - v) in ω × (0, T] u(·,0) = g1(·) v(·,0) = g2(·) in ω ⊂ R, 1≤d≤3 for given data k ∈ R, f, g1, g2 and a monotonically increasing ℘ ∈ C(R) ∩ C(-∞,0] ∪ (0,∞) satisfying ℘(0) = 0, which is only locally Hölder continuous with exponent p ∈ (0,1) at the origin, e.g., ℘(s) ≡ [s] . This lack of Lipschitz continuity at the origin limits the regularity of the unique solution {u,v} and leads to difficulties in the finite element error analysis.
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APA:
Barrett, J.W., & Knabner, P. (1997). Finite Element Approximation of the Transport of Reactive Solutes in Porous Media. Part 1: Error Estimates for Nonequilibrium Adsorption Processes. SIAM Journal on Numerical Analysis, 34(1), 201-227. https://dx.doi.org/10.1137/S0036142993249024
MLA:
Barrett, John W., and Peter Knabner. "Finite Element Approximation of the Transport of Reactive Solutes in Porous Media. Part 1: Error Estimates for Nonequilibrium Adsorption Processes." SIAM Journal on Numerical Analysis 34.1 (1997): 201-227.
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