On the finite element approximation of a semicoercive Stokes variational inequality arising in glaciology

Stokes variational inequalities arise in the formulation of glaciological problems involving contact. Two important examples of such problems are that of the grounding line of a marine ice sheet and the evolution of a subglacial cavity. In general, rigid modes are present in the velocity space, rend...

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Bibliographic Details
Main Authors: de Diego, Gonzalo G., Farrell, Patrick E., Hewitt, Ian J.
Format: Article in Journal/Newspaper
Language:unknown
Published: arXiv 2021
Subjects:
Numerical Analysis math.NA
FOS Mathematics
65N12, 65N15, 65N30, 86A40
Lagrange
Ice Sheet
Online Access:https://dx.doi.org/10.48550/arxiv.2108.00046
https://arxiv.org/abs/2108.00046
id ftdatacite:10.48550/arxiv.2108.00046
record_format openpolar
spelling ftdatacite:10.48550/arxiv.2108.00046 2023-05-15T16:40:47+02:00 On the finite element approximation of a semicoercive Stokes variational inequality arising in glaciology de Diego, Gonzalo G. Farrell, Patrick E. Hewitt, Ian J. 2021 https://dx.doi.org/10.48550/arxiv.2108.00046 https://arxiv.org/abs/2108.00046 unknown arXiv Creative Commons Attribution 4.0 International https://creativecommons.org/licenses/by/4.0/legalcode cc-by-4.0 CC-BY Numerical Analysis math.NA FOS Mathematics 65N12, 65N15, 65N30, 86A40 Article CreativeWork article Preprint 2021 ftdatacite https://doi.org/10.48550/arxiv.2108.00046 2022-03-10T13:37:33Z Stokes variational inequalities arise in the formulation of glaciological problems involving contact. Two important examples of such problems are that of the grounding line of a marine ice sheet and the evolution of a subglacial cavity. In general, rigid modes are present in the velocity space, rendering the variational inequality semicoercive. In this work, we consider a mixed formulation of this variational inequality involving a Lagrange multiplier and provide an analysis of its finite element approximation. Error estimates in the presence of rigid modes are obtained by means of a novel technique involving metric projections onto closed convex cones. Numerical results are reported to validate the error estimates and demonstrate the advantages of using a mixed formulation in a glaciological application. Article in Journal/Newspaper Ice Sheet DataCite Metadata Store (German National Library of Science and Technology) Lagrange ENVELOPE(-62.597,-62.597,-64.529,-64.529)
institution Open Polar
collection DataCite Metadata Store (German National Library of Science and Technology)
op_collection_id ftdatacite
language unknown
topic Numerical Analysis math.NA
FOS Mathematics
65N12, 65N15, 65N30, 86A40
spellingShingle Numerical Analysis math.NA
FOS Mathematics
65N12, 65N15, 65N30, 86A40
de Diego, Gonzalo G.
Farrell, Patrick E.
Hewitt, Ian J.
On the finite element approximation of a semicoercive Stokes variational inequality arising in glaciology
topic_facet Numerical Analysis math.NA
FOS Mathematics
65N12, 65N15, 65N30, 86A40
description Stokes variational inequalities arise in the formulation of glaciological problems involving contact. Two important examples of such problems are that of the grounding line of a marine ice sheet and the evolution of a subglacial cavity. In general, rigid modes are present in the velocity space, rendering the variational inequality semicoercive. In this work, we consider a mixed formulation of this variational inequality involving a Lagrange multiplier and provide an analysis of its finite element approximation. Error estimates in the presence of rigid modes are obtained by means of a novel technique involving metric projections onto closed convex cones. Numerical results are reported to validate the error estimates and demonstrate the advantages of using a mixed formulation in a glaciological application.
format Article in Journal/Newspaper
author de Diego, Gonzalo G.
Farrell, Patrick E.
Hewitt, Ian J.
author_facet de Diego, Gonzalo G.
Farrell, Patrick E.
Hewitt, Ian J.
author_sort de Diego, Gonzalo G.
title On the finite element approximation of a semicoercive Stokes variational inequality arising in glaciology
title_short On the finite element approximation of a semicoercive Stokes variational inequality arising in glaciology
title_full On the finite element approximation of a semicoercive Stokes variational inequality arising in glaciology
title_fullStr On the finite element approximation of a semicoercive Stokes variational inequality arising in glaciology
title_full_unstemmed On the finite element approximation of a semicoercive Stokes variational inequality arising in glaciology
title_sort on the finite element approximation of a semicoercive stokes variational inequality arising in glaciology
publisher arXiv
publishDate 2021
url https://dx.doi.org/10.48550/arxiv.2108.00046
https://arxiv.org/abs/2108.00046
long_lat ENVELOPE(-62.597,-62.597,-64.529,-64.529)
geographic Lagrange
geographic_facet Lagrange
genre Ice Sheet
genre_facet Ice Sheet
op_rights Creative Commons Attribution 4.0 International
https://creativecommons.org/licenses/by/4.0/legalcode
cc-by-4.0
op_rightsnorm CC-BY
op_doi https://doi.org/10.48550/arxiv.2108.00046
_version_ 1766031206205358080

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