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Semi-explicit discr...
Semi-explicit discretization schemes for weakly coupled elliptic-parabolic problems
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- Altmann, R. (author)
- Universität Augsburg,University of Augsburg
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- Maier, Roland, 1993 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,Chalmers tekniska högskola,Chalmers University of Technology,University of Gothenburg
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- Unger, B. (author)
- Universität Stuttgart,University of Stuttgart,Technische Universität Berlin
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(creator_code:org_t)
- American Mathematical Society (AMS), 2021
- 2021
- English.
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In: Mathematics of Computation. - : American Mathematical Society (AMS). - 0025-5718 .- 1088-6842. ; 90:329, s. 1089-1118
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Abstract
Subject headings
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- We prove first-order convergence of the semi-explicit Euler scheme combined with a finite element discretization in space for elliptic-parabolic problems which are weakly coupled. This setting includes poroelasticity, thermoelasticity, as well as multiple-network models used in medical applications. The semi-explicit approach decouples the system such that each time step requires the solution of two small and well-structured linear systems rather than the solution of one large system. The decoupling improves the computational efficiency without decreasing the convergence rates. The presented convergence proof is based on an interpretation of the scheme as an implicit method applied to a constrained partial differential equation with delay term. Here, the delay time equals the used step size. This connection also allows a deeper understanding of the weak coupling condition, which we accomplish to quantify explicitly.
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
- TEKNIK OCH TEKNOLOGIER -- Elektroteknik och elektronik -- Reglerteknik (hsv//swe)
- ENGINEERING AND TECHNOLOGY -- Electrical Engineering, Electronic Engineering, Information Engineering -- Control Engineering (hsv//eng)
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Keyword
- Elliptic-parabolic problem
- semi-explicit time discretization
- delay
- poroelasticity
- multiple-network
- finite-element methods
- computational multiscale methods
- linear
- poroelasticity
- fixed-stress
- stability
- equations
- model
- Mathematics
- semi-explicit time discretization
Publication and Content Type
- ref (subject category)
- art (subject category)
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