A posteriori error estimation and adaptivity for multiple-network poroelasticity

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Esaim-Probability and Statistics Pub Date : 2023-07-01 DOI:10.1051/m2an/2023033

Emilie Eliseussen, Marie E. Rognes, Travis B. Thompson

引用次数: 4

Abstract

The multiple-network poroelasticity (MPET) equations describe deformation and pressures in an elastic medium permeated by interacting fluid networks. In this paper, we (i) place these equations in the theoretical context of coupled elliptic–parabolic problems, (ii) use this context to derive residual-based a posteriori error estimates and indicators for fully discrete MPET solutions and (iii) evaluate the performance of these error estimators in adaptive algorithms for a set of test cases: ranging from synthetic scenarios to physiologically realistic simulations of brain mechanics.

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多网络孔隙弹性的后验误差估计与自适应

多网络孔隙弹性(MPET)方程描述了相互作用流体网络渗透的弹性介质中的变形和压力。在本文中，我们(i)将这些方程置于耦合椭圆-抛物线问题的理论背景中，(ii)使用此背景推导基于残差的后验误差估计和完全离散MPET解决方案的指标，以及(iii)评估这些误差估计器在自适应算法中的性能，用于一组测试用例:从合成场景到大脑力学的生理现实模拟。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Esaim-Probability and Statistics STATISTICS & PROBABILITY-

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original research and survey papers in the area of Probability and Statistics. It covers theoretical and practical aspects, in any field of these domains. Of particular interest are methodological developments with application in other scientific areas, for example Biology and Genetics, Information Theory, Finance, Bioinformatics, Random structures and Random graphs, Econometrics, Physics. Long papers are very welcome. Indeed, we intend to develop the journal in the direction of applications and to open it to various fields where random mathematical modelling is important. In particular we will call (survey) papers in these areas, in order to make the random community aware of important problems of both theoretical and practical interest. We all know that many recent fascinating developments in Probability and Statistics are coming from "the outside" and we think that ESAIM: P&S should be a good entry point for such exchanges. Of course this does not mean that the journal will be only devoted to practical aspects.