20 Result(s)
within
Takuya Tsu**o
Mathematics
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Article
Correction to: General theory of interpolation error estimates on anisotropic meshes
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Chapter and Conference Paper
Numerical Simulations of Semilinear Klein–Gordon Equation in the de Sitter Spacetime with Structure-Preserving Scheme
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-preserving scheme (SPS) in an earli...
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Article
Open AccessAnisotropic interpolation error estimates using a new geometric parameter
We present precise anisotropic interpolation error estimates for smooth functions using a new geometric parameter and derive inverse inequalities on anisotropic meshes. In our theory, the interpolation error i...
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Article
Open AccessA robust discontinuous Galerkin scheme on anisotropic meshes
Discontinuous Galerkin (DG) methods are extensions of the usual Galerkin finite element methods. Although there are vast amount of studies on DG methods, most of them have assumed shape-regularity conditions o...
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Article
Crouzeix–Raviart and Raviart–Thomas finite-element error analysis on anisotropic meshes violating the maximum-angle condition
We investigate the piecewise linear nonconforming Crouzeix–Raviart and the lowest order Raviart–Thomas finite-element methods for the Poisson problem on three-dimensional anisotropic meshes. We first give erro...
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Article
General theory of interpolation error estimates on anisotropic meshes
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 diameter of a simplex and a ge...
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Article
Error analysis of Crouzeix–Raviart and Raviart–Thomas finite element methods
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 estimations, we use the techniques d...
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Article
Finite element approximations of minimal surfaces: algorithms and mesh refinement
Finite element approximations of minimal surfaces are not always precise. They can even sometimes completely collapse. In this paper, we provide a simple and inexpensive method, in terms of computational cost,...
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Article
Approximating surface areas by interpolations on triangulations
We consider surface area approximations by Lagrange and Crouzeix-Raviart interpolations on triangulations. For Lagrange interpolation, we give an alternative proof for Young’s classical result that claims the ...
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Article
Extending Babuška-Aziz’s theorem to higher-order Lagrange interpolation
We consider the error analysis of Lagrange interpolation on triangles and tetrahedrons. For Lagrange interpolation of order one, Babuška and Aziz showed that squeezing a right isosceles triangle perpendicularl...
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Article
A priori error estimates for Lagrange interpolation on triangles
We present the error analysis of Lagrange interpolation on triangles. A new a priori error estimate is derived in which the bound is expressed in terms of the diameter and circumradius of a triangle. No geomet...
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Article
On the circumradius condition for piecewise linear triangular elements
We discuss the error analysis of linear interpolation on triangular elements. We claim that the circumradius condition is more essential than the well-known maximum angle condition for convergence of the finit...
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Article
A Babuška-Aziz type proof of the circumradius condition
In this paper the error of polynomial interpolation of degree 1 on triangles is considered. The circumradius condition, which is more general than the maximum angle condition, is explained and proved by the te...
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Article
Weak formulation of Hadamard variation applied to the filtration problem
Quantities defined using a solution of an elliptic boundary value problem may vary when the boundary of the domain is perturbed. Such a variation with respect to domain perturbation is called Hadamard variatio...
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Article
Convergence analysis of trial free boundary methods for the two-dimensional filtration problem
In this paper, we present a scheme of convergence analysis of trial free boundary methods for the two-dimensional filtration (or dam) problem. For the purpose we present a new variational principle of the filt...
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Article
Precise finite element error analysis by Yamamoto's explicit inversion formula for tridiagonal matrices – an extension of Babuška-Osborn's theorems
In this paper, we apply Yamamoto's explicit inversion formula for tridiagonal matrices to error analysis of the piecewise linear finite element method for two-point boundary value problems. Using the formula,...
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Article
Finite element approximations of parametrized strongly nonlinear boundary value problems
Nonlinear boundary value problems with parameters are called parametrized nonlinear boundary value problems. This paper studies a priori error estimates of finite element solutions of second order parametrized...
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Article
An application of the Kantorovich theoremto nonlinear finite element analysis
Finite element solutions of strongly nonlinear elliptic boundary value problems are considered. In this paper, using the Kantorovich theorem, we show that, if the Fréchet derivative of the nonlinear operator ...
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Article
Numerical verification of solutions of parametrized nonlinear boundary value problems with turning points
Nonlinear boundary value problems (NBVPs in abbreviation) with parameters are called parametrized nonlinear boundary value problems. This paper studies numerical verification of solutions of parametrized NBVPs...
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Article
Enlargement procedure for resolution of singularities at simple singular solutions of nonlinear equations
A solution of a nonlinear equation in Hilbert spaces is said to be a simple singular solution if the Fréchet derivative at the solution has one-dimensional kernel and cokernel. In this paper we present the enl...
