Development of the hybridized discontinuous method and its mathematical analysis

2016 Fiscal Year Final Research Report

• Project/Area Number: 26800089
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Waseda University
• Principal Investigator: Oikawa Issei 早稲田大学, 理工学術院, 次席研究員(研究院助教) (10637466)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 有限要素法 / 不連続ガレルキン法 / HDG法

Outline of Final Research Achievements

We developed and analyzed reduced-order hybridized discontinuous Galerkin (HDG) methods for Poission's equation and the Stokes equations. The proposed method is obtained by introducing the L2-orthogonal projection onto the finite element space of a numerical trace in the stabilization term of the standard HDG method. We mathematically proved that the order of convergence of the proposed method is optimal if we use a polygonal or polyhedral mesh satisfying the so-called chunkiness condition. For the mixed-type HDG method, we devised a new reduced-order scheme by introducing the L2-orthogonal projection in all the discretized equations. It was verified by numerical experiments that the new scheme achieves the optimal-order convergence, however, its error analysis is not provided.

Free Research Field

数値解析