Study on finite element methods for wave problems in unbounded domains and development of associated FEM softwares

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We need numerical simulations for construction of ocean structures and for development of high-performance sonar. First we mathematically established the validity of a simulation technique using the method called "finite element method." Next we obtained an optimal parameter which is used in the numerical simulation to speed up the simulations. We observed that the optimal parameter is effective for specific problems. Finally we mathematically proved the inequality called "Korn's inequality", which plays an essential role in analysis for validating a new simulation technique called "Hybridized discontinuous Galerkin finite element method" which will be used in numerical simulations of seismic waves, etc.