Problems involving irregularly shaped domains or embedded interfaces occur in a wide range of mathematical models. These include models in computational biology, fluid mechanics, and solidification. Numerical solutions for this type of problem can be difficult to obtain, and therefore a variety of methods have been devised to solve them....
Across a broad spectrum of mathematical models, problems arise that have irregular domains or contain embedded interfaces. The complexity due to the introduction of these interfaces makes it more difficult to develop efficient and accurate numerical methods for their solutions.
This thesis discusses modifications to the eXtended Finite Element Method...