Higher-order iterative decoupling for poroelasticity Higher-order iterative decoupling for poroelasticity

For the iterative decoupling of elliptic–parabolic problems such as poroelasticity, we introduce time discretization schemes up to order five based on the backward differentiation formulae. Its analysis combines techniques known from fixed-point iterations with the convergence analysis of the tempor...

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Bibliographic Details
Published inAdvances in computational mathematics Vol. 50; no. 6
Main Authors Altmann, Robert, Mujahid, Abdullah, Unger, Benjamin
Format Journal Article
LanguageEnglish
Published New York Springer US 01.12.2024
Springer Nature B.V
Subjects
Biomechanics
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Convergence
Decoupling
Discretization
Error analysis
Mathematical and Computational Biology
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Poroelasticity
Visualization
Iterative scheme
Decoupling
Poroelasticity
65J10
76S05
65M12
Higher-order discretization
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Summary:For the iterative decoupling of elliptic–parabolic problems such as poroelasticity, we introduce time discretization schemes up to order five based on the backward differentiation formulae. Its analysis combines techniques known from fixed-point iterations with the convergence analysis of the temporal discretization. As the main result, we show that the convergence depends on the interplay between the time step size and the parameters for the contraction of the iterative scheme. Moreover, this connection is quantified explicitly, which allows for balancing the single error components. Several numerical experiments illustrate and validate the theoretical results, including a three-dimensional example from biomechanics.
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ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-024-10200-0