How Long to Read Adaptive Methods in the Finite Element Exterior Calculus Framework

How Long Does it Take to Read Adaptive Methods in the Finite Element Exterior Calculus Framework?

It takes the average reader 1 hour and 40 minutes to read Adaptive Methods in the Finite Element Exterior Calculus Framework by Adam Mihalik

Assuming a reading speed of 250 words per minute. Learn more

Description

In this thesis we explore convergence theory for adaptive mixed finite element methods. In particular, we introduce an a posteriori error-indicator, and prove convergence and optimality results for the mixed formulation of the Hodge Laplacian posed on domains of arbitrary dimensionality and topology in R/n. After developing this framework, we introduce a new algorithm and extend our theory and results to problems posed on Euclidean hypersurfaces. We begin by introducing the finite element exterior calculus framework, which is the key tool allowing us to address the convergence proofs in such generality. This introduction focuses on the fundamentals of the well-developed a priori theory and the results needed to extend the core of this theory to problems posed on surfaces. A basic set of results needed to develop adaptivity in this framework is also established. We then introduce an adaptive algorithm, and show convergence using this infrastructure as a tool to generalize existing finite element theory. The algorithm is then shown to be computationally optimal through a series of complexity analysis arguments. Finally, a second algorithm is introduced for problems posed on surfaces, and our original convergence and optimality results are extended using properties of specific geometric maps between surfaces

How long is Adaptive Methods in the Finite Element Exterior Calculus Framework?

Adaptive Methods in the Finite Element Exterior Calculus Framework by Adam Mihalik is 100 pages long, and a total of 25,000 words.

This makes it 34% the length of the average book. It also has 31% more words than the average book.

How Long Does it Take to Read Adaptive Methods in the Finite Element Exterior Calculus Framework Aloud?

The average oral reading speed is 183 words per minute. This means it takes 2 hours and 16 minutes to read Adaptive Methods in the Finite Element Exterior Calculus Framework aloud.

What Reading Level is Adaptive Methods in the Finite Element Exterior Calculus Framework?

Adaptive Methods in the Finite Element Exterior Calculus Framework is suitable for students ages 10 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

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