Stability and discretization error analysis for the Cahn-Hilliard system via relative energy estimates
- Publication type:
- Journal article
- Metadata:
-
- Autoren
- Aaron Brunk
- Herbert Egger
- Oliver Habrich
- Maria Lukacova-Medvidova
- Autoren-URL
- https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=fis-test-1&SrcAuth=WosAPI&KeyUT=WOS:000986324300002&DestLinkType=FullRecord&DestApp=WOS_CPL
- DOI
- 10.1051/m2an/2023017
- eISSN
- 2804-7214
- Externe Identifier
- Clarivate Analytics Document Solution ID: G0RF2
- ISSN
- 2822-7840
- Ausgabe der Veröffentlichung
- 3
- Zeitschrift
- ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS
- Schlüsselwörter
- A priori error analysis
- nonlinear stability analysis
- optimal error estimates
- variational methods
- Cahn-Hilliard
- Paginierung
- 1297 - 1322
- Datum der Veröffentlichung
- 2023
- Status
- Published
- Titel
- Stability and discretization error analysis for the Cahn-Hilliard system <i>via</i> relative energy estimates
- Sub types
- Article
- Ausgabe der Zeitschrift
- 57
Data source: Web of Science (Lite)
- Other metadata sources:
-
- Abstract
- <jats:p>The stability of solutions to the Cahn–Hilliard equation with concentration dependent mobility with respect to perturbations is studied by means of relative energy estimates. As a by-product of this analysis, a weak-strong uniqueness principle is derived on the continuous level under realistic regularity assumptions on strong solutions. The stability estimates are further inherited almost verbatim by appropriate Galerkin approximations in space and time. This allows to derive sharp bounds for the discretization error in terms of certain projection errors and to establish order-optimal <jats:italic>a priori</jats:italic> error estimates for semi- and fully discrete approximation schemes. Numerical tests are presented for illustration of the theoretical results.</jats:p>
- Date of acceptance
- 2023
- Autoren
- Aaron Brunk
- Herbert Egger
- Oliver Habrich
- Mária Lukáčová-Medviďová
- DOI
- 10.1051/m2an/2023017
- eISSN
- 2804-7214
- ISSN
- 2822-7840
- Ausgabe der Veröffentlichung
- 3
- Zeitschrift
- ESAIM: Mathematical Modelling and Numerical Analysis
- Online publication date
- 2023
- Paginierung
- 1297 - 1322
- Datum der Veröffentlichung
- 2023
- Status
- Published
- Herausgeber
- EDP Sciences
- Herausgeber URL
- http://dx.doi.org/10.1051/m2an/2023017
- Datum der Datenerfassung
- 2023
- Titel
- Stability and discretization error analysis for the Cahn–Hilliard system <i>via</i> relative energy estimates
- Ausgabe der Zeitschrift
- 57
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