Research and development on computing schemes for systems including liquid flows

1.（1）已有一种由一位研究者和另一位研究者共同得到的用低阶多项式有限元求解多个流动的格式，因此需要用更多的高阶多项式构造一种新的格式。这是由海津写的报告完成的。（2）采用特征线法追踪液流粒子，成功地计算了两种流动的界面（Fujima）。（3）考虑了含液体流动和热场的系统的最优化问题。2.弹性波在Neumann边界的情况下考虑弹性波，采用Lax和菲利普斯的散射理论，并考虑Majda型散射核。3.一般边值问题及其反问题将任意多网格点法应用于一般边值问题的反问题。然后将这一结果应用于Laplace-Poisson方程（Onishe）的反问题。

1.Scheme for liquid flows(1)Already, there exists a scheme for multi-flows using finite element of low order degree of polynomials obtained by one of investigator together with other researcher, so it is needed to construct a new scheme for the same target using more higher order polynomials. It is done by a report written by Kaizu.(2)Characteristic method is applied to pursuit liquid flow particles, also interface of two flows are computed in a successful way (Fujima).(3)Optimal problems are considered for a system including liquid flows, including heat fields. Then in computation the shape of bodies are changed so nicely (Azegami)2.Elastic wavesElastic waves are considered in the case of the Neumann boundary, a scattering theory of Lax and Phillips, And the scattering kernel of the Majda type are considered. Some difficulty is solved in this situation (Soga)3.General boundary value problems and their inverse problemsAn arbitrarily many mesh points method is applied to the inverse problem, which appears in solving general boundary value problems. Then this good result is applied to the inverse problem for the Laplace-Poisson equation (Onishe).