Journal of Computational and Applied Mathematics 429 2023年9月 [査読有り]
For conforming finite element approximations of the Laplacian eigenfunctions, a fully computable guaranteed error bound in the L2 norm sense is proposed. The bound is based on the a priori error estimate for the Galerkin projection of the conformi...
Journal of Computational and Applied Mathematics 425 2023年6月 [査読有り]
This paper considers the finite element solution of the boundary value problem of Poisson's equation and proposes a guaranteed local error estimation based on the hypercircle method. Compared to the existing literature on qualitative error estimat...
For compact self-adjoint operators in Hilbert spaces, two algorithms are proposed to provide fully computable a posteriori error estimate for eigenfunction approximation. Both algorithms apply well to the case of tight clusters and multiple eigenv...
In this paper, a robust and efficient algorithm is proposed to calculate the intersection points of two planar algebraic curves with guaranteed tolerance. The proposed method takes advantage of the fundamental methods in the fields of CAGD, soluti...
Communications in Nonlinear Science and Numerical Simulation 108 2022年5月 [査読有り]
This paper proposes a computer-assisted solution existence verification method for the stationary Navier–Stokes equation over general 3D domains. The proposed method verifies that the exact solution as the fixed point of the Newton iteration exist...
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