Mathematical Sciences and Computer Research: Higher Order Finite Element Methods and Adaptive Approaches

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The investigator and his colleagues continue their study and development of highly accurate finite element methods for computing solutions of partial differential equations. They have shown in previous work that high degree methods, such as the h-p version of the finite element method, are very effective. Recently these methods have been implemented in various engineering programs (inclusive of commercial). The research will concentrate on mathematical and numerical problems leading to the reliable solution of problems of solid mechanics with important applications in engineering, such as fractures in 3- dimensional bodies, modelling of plates and shells, etc. The goal of the research is to establish mathematical results that will be used in the computer analysis of engineering problems. These results will allow to be developed highly effective computational methods for broad applications in research and commercial computer codes that are widely used in engineering science and practice.