【国際交流・公開研究セミナー】The Finite Element Method for the Boundary Value Problem with Strong Singularity of Solution
講演者:Dr. Victor A. Rukavishnikov教授
Victor A. Rukavishnikov教授(ロシア科学アカデミー極東支部計算センター物理・工学における数学的モデリング研究所所長)が来日される機会に,最近,物理・工学の多くの分野において注目されている有限要素法に関し,種々の複雑な境界値問題への応用について講演をお願いいたしました.是非ご参集ください.
アブストラクト:
Mathematical models for a number of physical processes lead to the differential problems in which the strong singularity of solution is caused by the singularity of initial data (the coefficients of the equation, the right hand sides of the equation and boundary conditions). For the boundary value problem of this type, for which the generalized (weak) solution can not be defined, or it does not have necessary regularity, we offered to define the solution as the -generalized one. Such a concept of solution led to distinction of two classes of boundary value problems: the problems with co-ordinated and non-co-ordinated degeneration of initial data. For these classes of problems this approach allowed to investigate the existence, uniqueness, coercivity, differential properties of the -generalized solution in the weighted Sobolev spaces. We construct and investigate the h-version and the h-p-version of the finite element method for these problems. We introduce the special regularizor and the finite element space which contains the singular functions, having the singularity depending on the space, to which the -generalized solution of the problem belongs. Using these elements we prove the estimate of the rate of convergence of the approximate solution to the exact -generalized solution in the norm of the weighted space. Numerical analysis of the modeling problems with singularity was made with elements of parallelizing the process of computing.
講演終了後,懇親会を予定しております.
連絡先:中央大学理工学部電気電子情報通信工学科
小林 一哉
電話:03-3817-1869