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Adaptive Quarklet Schemes: Tree Approximation and Optimal Convergence

This thesis is concerned with so-called quarklets and their properties. In particular, we investigate near-optimal approximations of explicitly and implicitly given L_2-functions with hp tree structures based on quarklets. We develop several adaptive methods in the context of partial differential eq...

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Main Author: Vogel, Dorian
Contributors: Dahlke, Stephan (Prof. Dr.) (Thesis advisor)
Format: Doctoral Thesis
Language:English
Published: Philipps-Universität Marburg 2024
Subjects:
Signal Analysis
Adaptive Verfahren
Wavelets
Mathematik
Operator Equations
Optimal Convergence
Partielle Differentialgleichungen
Quarklets
Partial Differential Equations
Frames
Multiwavelets
Numerische Mathematik
Numerical Analysis
hp-Methods
Operatorgleichungen
Adaptive Schemes
Mathematics
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Summary:This thesis is concerned with so-called quarklets and their properties. In particular, we investigate near-optimal approximations of explicitly and implicitly given L_2-functions with hp tree structures based on quarklets. We develop several adaptive methods in the context of partial differential equations and demonstrate their high order convergence rates in numerical experiments.
Physical Description:186 Pages
DOI:10.17192/z2024.0477

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