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Associate Professor
Numerical Analysis
Research interests
Numerical and mathematical analysis of PDEs, Navier-Stokes equations, Non-standard boundary conditions, Finite element method
Current research

I am interested in mathematical justification of numerical simulations, in which it is usually impossible to directly compute exact solutions of mathematical models. The main aim is to rigorously prove that numerical solutions, obtained via some approximation or discretization, are indeed close to exact ones. Moreover, in case exact solutions themselves are not well understood, I would like to establish their existence and uniqueness by mathematical analysis. More concretely, I have been studying the finite element method to PDEs, especially non-standard boundary value problems (e.g., frictional BCs and generalized Robin BCs) of the Navier-Stokes equations. Recently I am also focused on mathematical analysis of the primitive equations in oceanic or atmospheric dynamics, and on finite element analysis by the maximum-norm.

Selected publications
  1. T. Kashiwabara: "Finite element method for Stokes equations under leak boundary condition of friction type", SIAM J. Numer. Anal. 51 (2013), pp. 2448--2469.
  2. T. Kashiwabara: "On a strong solution of the non-stationary Navier-Stokes equations under slip or leak boundary conditions of friction type", J. Differential Equations 254 (2013), pp. 756--778.
  3. T. Kashiwabara, C.M. Colciago, L. Dedè, and A. Quarteroni: "Well-posedness, regularity, and convergence analysis of the finite element approximation of a generalized Robin boundary value problem", SIAM J. Numer. Anal. 53 (2015), pp. 105--126.
  4. T. Kashiwabara, I. Oikawa, and G. Zhou: "Penalty method with P1/P1 Finite element approximation for the Stokes equations under the slip boundary condition", Numer. Math. 134 (2016), pp. 705--740.
  5. M. Hieber and T. Kashiwabara: "Global strong well-posedness of the three dimensional primitive equations in the $L^p$-setting", Arch. Rational Mech. Anal. 221 (2016), pp. 1077--1115.