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Kashiwabara Lab
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The lab provides mathematical guarantees that numerical simulations are correct.
AboutAbout the lab
Verifying simulation results with mathematics
Kashiwabara Lab works in numerical analysis, studying the mathematical justification of numerical simulations performed on computers.
Its goal is to prove that the approximate solutions obtained from numerical simulations are truly close to the exact solutions of the mathematical models, thereby guaranteeing the correctness of approximation and discretization.
The main subject is partial differential equations, in particular the Navier-Stokes equations, the fundamental equations of fluid dynamics.
Recently, the lab has also become interested in the mathematical analysis of the Primitive equations that arise in geophysics, and in finite element analysis in the maximum norm.
Key terms
- Discretization
- The process of replacing a continuous quantity with values at discrete points, so that it can be computed on a computer
- Navier-Stokes equations
- The fundamental partial differential equations that describe the motion of fluids such as water and air
- Finite element method
- A method for finding approximate solutions of equations by dividing the domain of interest into small elements such as triangles
ResearchResearch themes
The lab studies the numerical analysis and mathematical analysis of partial differential equations. It aims to prove that approximate solutions are close to exact solutions, and thereby to give a mathematical guarantee of the correctness of numerical simulations.
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MembersFaculty
- Associate ProfessorTakahito KashiwabaraPublications ↗
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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: “Karmansche Wirbelstr kleine Re” Jürgen Wagner / CC BY-SA 4.0 (cropped)
- Numerical Analysis of the Navier-Stokes Equations: “Crouzeix-Raviart-Finite-Elemente-Lösung” Grawiuton / CC0 (cropped)
- Related lab (Saito Lab): “Example finite element mesh, for illustrating the concept” SamitchSandia / CC BY-SA 4.0 (cropped)
- Related lab (Hasegawa Lab): “Lambda cube” Денис Москвин / Public domain (cropped)
- Related lab (Shimomura Lab): “Traveling wave” P.wormer / CC BY-SA 3.0 (cropped)
- Related lab (Matui Lab): “Cantors cube” User:Solkoll / Public domain (cropped)
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