27 citations · 157 across the 31 of their papers we have counts for
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Structure-preserving numerical calculation of wave equation for a vector field
Takuya Tsuchiya
For the Proca equation, which is a wave equation for a vector field, we derive the canonical formulation including constraints from the Stueckelberg action and propose discrete equ…
Quantitative evaluations of stability and convergence for solutions of semilinear Klein--Gordon equation
Takuya Tsuchiya, Makoto Nakamura
We perform some simulations of the semilinear Klein--Gordon equation with a power-law nonlinear term and propose each of the quantitative evaluation methods for the stability and c…
Numerical accuracy and stability of semilinear Klein--Gordon equation in de Sitter spacetime
Takuya Tsuchiya, Makoto Nakamura
Numerical simulations of the semilinear Klein--Gordon equation in the de Sitter spacetime are performed. We use two structure-preserving discrete forms of the Klein--Gordon equatio…
Numerical simulations of semilinear Klein--Gordon equation in the de Sitter spacetime with structure-preserving scheme
Takuya Tsuchiya, Makoto Nakamura
We perform some simulations of the semilinear Klein--Gordon equation in the de Sitter spacetime. We reported the accurate numerical results of the equation with the structure-prese…
Anisotropic interpolation error estimates using a new geometric parameter
Hiroki Ishizaka, Kenta Kobayashi, Takuya Tsuchiya
We present precise anisotropic interpolation error estimates for smooth functions using a new geometric parameter and derive inverse inequalities on anisotropic meshes. In our theo…
Lectures on error analysis of interpolation on simplicial triangulations without the shape-regularity assumption, Part 2: Lagrange interpolation on tetrahedrons
Kenta Kobayashi, Takuya Tsuchiya
This is the second lecture note on the error analysis of interpolation on simplicial elements without the shape regularity assumption (the previous one is arXiv:1908.03894). In thi…