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14 papers · 1 filter
A new geometric condition equivalent to the maximum angle condition for tetrahedrons
Hiroki Ishizaka, Kenta Kobayashi, Ryo Suzuki +1
For a tetrahedron, suppose that all internal angles of faces and all dihedral angles are less than a fixed constant that is smaller than . Then, it is said to satisfy the ma…
A new efficient approximation scheme for solving high-dimensional semilinear PDEs: control variate method for Deep BSDE solver
Akihiko Takahashi, Yoshifumi Tsuchida, Toshihiro Yamada
This paper introduces a new approximation scheme for solving high-dimensional semilinear partial differential equations (PDEs) and backward stochastic differential equations (BSDEs…
Numerical methods for backward stochastic differential equations: A survey
Jared Chessari, Reiichiro Kawai, Yuji Shinozaki +1
Backward Stochastic Differential Equations (BSDEs) have been widely employed in various areas of social and natural sciences, such as the pricing and hedging of financial derivativ…
Crouzeix-Raviart and Raviart-Thomas finite-element error analysis on anisotropic meshes violating the maximum-angle condition
Hiroki Ishizaka, Kenta Kobayashi, Takuya Tsuchiya
We investigate the piecewise linear nonconforming Crouzeix-Raviar and the lowest order Raviart-Thomas finite-element methods for the Poisson problem on three-dimensional anisotropi…
General theory of interpolation error estimates on anisotropic meshes
Hiroki Ishizaka, Kenta Kobayashi, Takuya Tsuchiya
We propose a general theory of estimating interpolation error for smooth functions in two and three dimensions. In our theory, the error of interpolation is bound in terms of the d…
Error analysis of Crouzeix-Raviart and Raviart-Thomas finite element methods
Kenta Kobayashi, Takuya Tsuchiya
We discuss the error analysis of the lowest degree Crouzeix-Raviart and Raviart-Thomas finite element methods applied to a two-dimensional Poisson equation. To obtain error estimat…