Superconvergent HDG methods for the biharmonic equation

2021 Fiscal Year Final Research Report

• Project/Area Number: 20K22300
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Multi-year Fund
• Review Section: 0201:Algebra, geometry, analysis, applied mathematics,and related fields
• Research Institution: University of Tsukuba
• Principal Investigator: Oikawa Issei 筑波大学, 数理物質系, 准教授 (10637466)
• Project Period (FY): 2020-09-11 – 2022-03-31
• Keywords: 数値解析

Outline of Final Research Achievements

We studied the superconvergence of the hybridizable discontinuous Galerkin method (HDG) for the biharmonic equation. Using the idea of introducing a hybrid variable for the gradient of the exact solution, we obtained a new HDG formulation. Numerical experiments of the method were carried out, and we observed that the orders of convergence in three of the four variables were optimal.

Free Research Field

数値解析

Academic Significance and Societal Importance of the Research Achievements

本研究では重調和方程式のHybridizable Discontinuous Galerkin (HDG) 法の超収束性の研究を数学的な立場から行い，一定の成果を得た．HDG法の研究において超収束性は主要なテーマであるため，学術的な意義があると考える．さらに，本研究の結果は将来的により優れた偏微分方程式の数値計算手法の開発へとつながることが期待できる．