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An Adaptive Surface Finite Element Method for the Laplace-Beltrami Equation
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
2017 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
En adaptiv finita elementmetod för Laplace-Beltrami ekvationen (Swedish)
Abstract [en]

In this thesis, we present an adaptive surface finite element method for the Laplace-Beltrami equation. The equation is known as the manifold equivalent of the Laplace equation. A surface finite element method is formulated for this partial differential equation which is implemented in FEniCS, an open source software project for automated solutions of differential equations. We formulate a goal-oriented adaptive mesh refinement method based on a posteriori error estimates which are established with the dual-weighted residual method. Some computational examples are provided and implementation issues are discussed.

Abstract [sv]

I den här rapporten presenterar vi en adaptiv finite elementmetod för Laplace-Beltrami ekvationen. Ekvationen är känd som Laplace ekvation på ytor. En finita elementmetod för ytor formuleras för denna partiella differentialekvation vilken implementeras i FEniCS, en open source mjukvara för automatiserad lösning av differentialekvationer. Vi formulerar en mål-orienterad adaptiv nätförfinings-metod baserad på a posteriori feluppskattningar etablerade med hjälp av metoden för dual-viktad residual. Beräkningsexempel presenteras och implementeringen diskuteras

Place, publisher, year, edition, pages
2017.
Series
TRITA-MAT-E ; 2017:05
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-202764OAI: oai:DiVA.org:kth-202764DiVA, id: diva2:1078803
Subject / course
Scientific Computing
Educational program
Master of Science - Applied and Computational Mathematics
Supervisors
Examiners
Available from: 2017-03-06 Created: 2017-03-06 Last updated: 2017-10-29Bibliographically approved

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CiteExportLink to record
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