Date of Award

Summer 2021

Document Type


Degree Name

Master of Arts (MA)


Mathematics and Statistics

First Advisor

Vincent Martinez

Second Advisor

Animikh Biswas

Academic Program Adviser

Vincent Martinez


This thesis develops the finite element method, constructs local approximation operators, and bounds their error. Global approximation operators are then constructed with a partition of unity. Finally, an application of these operators to data assimilation of the two-dimensional Navier-Stokes equations is presented, showing convergence of an algorithm in all Sobolev topologies.



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