An improved error bound for a Lagrange-Galerkin method for contaminant transport with non-lipschitzian adsorption kinetics

Barrett JW, Knabner P (1998)

Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 1998

Journal

SIAM Journal on Numerical Analysis Society for Industrial and Applied Mathematics

Publisher: Society for Industrial and Applied Mathematics

Book Volume: 35

Pages Range: 1862-1882

Journal Issue: 5

URI: https://www1.am.uni-erlangen.de/research/publications/Jahr_1998/1998_BarrettKn_ImprErrBoundForLagrGalerkMethForContTranspNonLipAdsKinet

Abstract

In this paper we consider the Lagrange-Galerkin finite element approximation by continuous piecewise linears in space of the following problem: Given ω ⊂ R, 1 ≤ d ≤ 3, find u(x, t) and v(x, t) such that ∂u + ∂v - ∇.(D ∇u) + q.∇u = f in ω × (0, T], dv = k(φ(u) - v) in ω × (0, T], u(x, 0) = g(x), v(x, 0) = g(x) ∀ x ∈ ω, with periodic boundary conditions. Here k ∈ R and the spatial differential operator is uniformly elliptic, but φ ∈ C(R) ∩ C (-∞, 0] ∪ (0, ∞) is a monotonically increasing function satisfying φ(0) = 0, which is only locally Hölder continuous, with exponent p ∈ (0, 1) at the origin; e.g., ∈(s) := [s] . We obtain error bounds which improve on those in the literature.

Authors with CRIS profile

Peter Knabner Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

Involved external institutions

Imperial College London / The Imperial College of Science, Technology and Medicine GB United Kingdom (GB)

How to cite

APA:

Barrett, J.W., & Knabner, P. (1998). An improved error bound for a Lagrange-Galerkin method for contaminant transport with non-lipschitzian adsorption kinetics. SIAM Journal on Numerical Analysis, 35(5), 1862-1882.

MLA:

Barrett, John W., and Peter Knabner. "An improved error bound for a Lagrange-Galerkin method for contaminant transport with non-lipschitzian adsorption kinetics." SIAM Journal on Numerical Analysis 35.5 (1998): 1862-1882.

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