Date of Award

2021-08-01

Degree Name

Master of Science

Department

Mathematical Sciences

Advisor(s)

Natasha S. Sharma

Abstract

Adaptive mesh refinement techniques have become an indispensable tool in achieving accurate and efficiently computed solutions to problems which require impractically fine uniform meshes to obtain an accurate approximation. The adaptive algorithm involves a recursive application of SOLVE-ESTIMATE-MARK-REFINE steps where in particular the step `ESTIMATE' involves computing a posteriori error estimator based on only the numerical solution and the data of the problem. Over the years, several a posteriori error estimators have been developed and successfully applied but often times, the choice of estimator is ill suited for the problem at hand. In this research, we present two estimators namely the residual-based estimator and the gradient recovery type estimator and illustrate the suitability of these estimators for different problems at hand. We also provide the foundation for data-driven adaptive mesh refinement strategies based on Reinforcement learning (RL) with a focus on the Q-learning algorithm which is a fundamental learning algorithm in RL.

Language

en

Provenance

Recieved from ProQuest

File Size

105 p.

File Format

application/pdf

Rights Holder

Augustine Twumasi

Included in

Mathematics Commons

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