The investigator and his colleagues study the superconvergence phenomenon and its recovery of several major computational methods in science and engineering. The research objectives include (1) to develop a superconvergence recovery technique and associated error estimator for discontinuous Galerkin method; (2) to enhance the eigenvalue approximation by recovery techniques; and (3) to investigate superconvergence phenomena of p- version/spectral collocation methods. Some recent mathematical theory in finite element superconvergence, discontinuous Galerkin methods, as well as domain variation techniques in the PDE theory and classical results in approximation theory will be employed in the project.
The study is of great importance for the adaptive design of computational algorithms and has a direct application in engineering computation. The success of the project will bridge a gap between engineering practice and mathematical theoretical development and widen the knowledge in the scientific community. The project has solid multi- and interdisciplinary contents and wide application in the software industry.
