FINITE ELEMENT APPROXIMATION OF THE TRANSPORT OF REACTIVE SOLUTES IN POROUS MEDIA. PART II: ERROR ESTIMATES FOR EQUILIBRIUM ADSORPTION PROCESSES∗
FINITE ELEMENT APPROXIMATION OF THE TRANSPORT OF REACTIVE SOLUTES IN POROUS MEDIA. PART II: ERROR ESTIMATES FOR EQUILIBRIUM ADSORPTION PROCESSES∗
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多孔介质中反应性溶质输运的有限元近似。第二部分：平衡吸附过程的误差估计*
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发表时间：
1997
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通讯作者：
P. Knabner
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作者：
J. Barrett;P. Knabner
在本文中，我们分析了一个完全实用的分段线性有限元近似，涉及数值积分，向后欧拉时间离散化，以及可能的正则化和松弛在多孔介质中反应性溶质输运模型中出现的退化抛物方程：找到u（x, t）使得∂tu+∂t[φ(u)]−∆u = f在Ω× （0, t）中，u = 0在∂Ω× （0, t）中u（·，0）= g（·）在Ω中，对于已知数据Ω∧R， 1≤d≤3,f, g，以及一个单调增长的φ∈C0(R)∩C1(−∞,0)∪(0,∞)满足φ(0) = 0，且仅在局部Hölder连续且指数p∈(0,1)在原点；例如，φ(s)≡[s]p+。由于在原点处缺乏Lipschitz连续性，限制了唯一解u的正则性，给有限元误差分析带来困难。
In this paper we analyze a fully practical piecewise linear finite element approximation involving numerical integration, backward Euler time discretization, and possibly regularization and relaxation of the following degenerate parabolic equation arising in a model of reactive solute transport in porous media: find u(x, t) such that ∂tu+ ∂t[φ(u)]−∆u = f in Ω× (0, T ], u = 0 on ∂Ω× (0, T ] u(·, 0) = g(·) in Ω for known data Ω ⊂ R, 1 ≤ d ≤ 3, f , g, and a monotonically increasing φ ∈ C0(R) ∩ C1(−∞, 0] ∪ (0,∞) satisfying φ(0) = 0, which is only locally Hölder continuous with exponent p ∈ (0, 1) at the origin; e.g., φ(s) ≡ [s]p+. This lack of Lipschitz continuity at the origin limits the regularity of the unique solution u and leads to difficulties in the finite element error analysis.