Development of the hybridized discontinuous method and its mathematical analysis
| Project/Area Number |
26800089
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Waseda University |
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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)
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 有限要素法 / 不連続ガレルキン法 / HDG法 / 数値解析 / 不連続Galerkin法 / ハイブリッド法 |
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| 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.
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Report
(4 results)
Research Products
(15 results)
