In this paper, a numerical verification method is presented for second-order semilinear elliptic boundary value problems on arbitrary polygonal domains. Based on the Newton-Kantorovich theorem, our method can prove the existence and local uniquene...
JOURNAL OF MATHEMATICAL SCIENCES-THE UNIVERSITY OF TOKYO 17(1) 27-78 2010年 [査読有り]
We give some fundamental results on the error constants for the piecewise constant interpolation function and the piecewise linear one over triangles. For the piecewise linear one, we mainly analyze the conforming case, but the present results als...
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 196(37-40) 3750-3758 2007年 [査読有り]
We give some fundamental results on the error constants for the piecewise constant interpolation function and the piecewise linear one over triangles. For the piecewise linear one, we mainly analyze the conforming case, but some results are also g...
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS 23(1) 75-82 2006年2月 [査読有り]
We explicitly determine the Babuska-Aziz constant, which plays an essential role in the interpolation error estimation of the linear triangular finite element. The equation for determination is the transcendental equation t + tan t = 0, so that th...
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