Data structures and implementation of an adaptive hp finite element method

For a fully adaptive hp finite element programme to be implemented it is necessary to implement n-irregular meshes efficiently. This requires a sufficiently flexible data structure to be implemented. Because such flexibility is required, the traditional array based approach cannot be used because of its limited applicability. In this thesis this traditional approach has been replaced by an object orientated design and implementation. This leads to an implementation that can be extended easily and safely to include other problems for which it was not originally designed.;The problems with maintaining continuity on such a diverse variety of meshes and how continuity is maintained are discussed. Then the main structure of the mesh is described in the form of domain, subdomains and elements. These are used in conjunction with constraint mappings to give a conforming approximation even with the most irregular of meshes.;There are several varieties of matrix generated by the method each with its own problems of storage. Sparse matrices, with perhaps more than 95% of zero entries, need to be used along side dense matrices. In this thesis an object oriented matrix library is implemented that enables this variety of matrices to be used.;An hp finite element algorithm is then implemented using the data structures, and is tested on a range of test problems. The method is shown to be effective on these problems.