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Oikawa Lab
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A numerical analysis lab that uses mathematics to study the finite element method and discontinuous Galerkin methods.
AboutAbout the lab
Numerical analysis of finite element and discontinuous Galerkin methods.
The Oikawa Lab studies numerical analysis, particularly the finite element method and discontinuous Galerkin methods.
Its research keywords also include numerical computation, error analysis, partial differential equations, and domain decomposition methods.
The faculty list of the Mathematics Degree Program introduces the professor as an Associate Professor in the Information group.
Key terms
- Finite element method
- A method for computing approximate solutions of partial differential equations on a computer
- Partial differential equation
- An equation that expresses relationships among the rates of change (partial derivatives) of a function of several variables
- HDG method
- Short for hybridized discontinuous Galerkin method. A type of discontinuous Galerkin method
ResearchResearch themes
As a faculty member of the Mathematics Degree Program, the professor studies the numerical analysis of the finite element method and discontinuous Galerkin methods. Recently, the lab has worked on HDG methods and their domain decomposition methods, as well as Galerkin methods for ordinary differential equations.
*Illustrative imageNumerical Analysis of HDG Methods
The lab studies HDG methods, a type of discontinuous Galerkin method. There is a paper on flux-based HDG methods, and the lab also publishes materials on HDG code for use with FreeFEM and FEniCS.
*Illustrative imageHDG Methods and Domain Decomposition
The lab is developing iterative domain decomposition methods for HDG methods. It presented a Schwarz-type algorithm based on non-overlapping domain decomposition at ICIAM 2023.
*Illustrative imageGalerkin Methods for Ordinary Differential Equations
In joint research, the lab studies and presents work on the superconvergence of the continuous Galerkin method for ordinary differential equations, and on turbo post-processing of continuous and discontinuous Galerkin methods.
MembersFaculty
- Associate ProfessorIssei Oikawa
VoicesStudent voices
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Crouzeix-Raviart-Finite-Elemente-Lösung” Grawiuton / CC0 (cropped)
- Numerical Analysis of HDG Methods: “Finite element mesh” Bruno Sudret / CC BY 4.0 (cropped)
- HDG Methods and Domain Decomposition: “Rack of Cisco Hyperflex HXAF 240c M5 nodes” Btrs / CC BY-SA 4.0 (cropped)
- Galerkin Methods for Ordinary Differential Equations: “Texas Instruments SR-10 Calculator” Mister rf / CC BY-SA 4.0 (cropped)
- Related lab (照井 章 研究室): “Kreis Maxima” Birgit 18 / CC BY-SA 4.0 (cropped)
- Related lab (桑原 敏郎 研究室): “Matematička gimnazija - Mathematical Gymnasium Belgrade - MGB - Physics Laboratory 1” MGB / Public domain (cropped)
- Related lab (竹山 美宏 研究室): “Portal Math Banner Background ka” User:Alsandro / CC0 (cropped)
- Related lab (竹内 耕太 研究室): “Classroom blackboard at Cornell University, Ithaca, NY 25” LBM1948 / CC BY-SA 4.0 (cropped)
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