Applications of Mathematics 63(4) 381-397 2018年8月 [査読有り]
The non-conforming linear (P1) triangular FEM can be viewed as a kind of the discontinuous Galerkin method, and is attractive in both the theoretical and practical purposes. Since various error constants must be quantitatively evaluated for its ac...
Applications of Mathematics 63(3) 367-379 2018年6月 [査読有り]
The paper develops an explicit a priori error estimate for finite element solution to nonhomogeneous Neumann problems. For this purpose, the hypercircle over finite element spaces is constructed and the explicit upper bound of the constant in the ...
Japan Journal of Industrial and Applied Mathematics 35(1) 335-354 2018年3月 [査読有り]
An algorithm is proposed to give explicit lower bounds of the Stokes eigenvalues by utilizing two nonconforming finite element methods: Crouzeix–Raviart (CR) element and enriched Crouzeix–Raviart (ECR) element. Compared with the existing literatur...
APPLIED MATHEMATICS AND COMPUTATION 319 693-701 2018年2月 [査読有り]
For the quadratic Lagrange interpolation function, an algorithm is proposed to provide explicit and verified bound for the interpolation error constant that appears in the interpolation error estimation. The upper bound for the interpolation const...
APPLIED MATHEMATICS AND COMPUTATION 267 341-355 2015年9月 [査読有り]
For eigenvalue problems of self-adjoint differential operators, a universal framework is proposed to give explicit lower and upper bounds for the eigenvalues. In the case of the Laplacian operator, by applying Crouzeix-Raviart finite elements, an ...
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