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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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연구자들이 자신의 연구와 전문성을 널리 알리고, 새로운 협력의 기회를 만들 수 있는 네트워킹 공간이에요.
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We propose and analyze two-scale product approximation for semilinear heat equations in the mixed finite element method. In order to efficiently resolve nonlinear algebraic equations resulting from the mixed method for semilinear parabolic problems, we treat the nonlinear terms using some interpolation operator and exploit a two-scale grid algorithm.
With this scheme, the nonlinear problem is reduced to a linear problem on a fine scale mesh without losing overall accuracy of the final system.
We derive optimal order L ∞ ((0,T];L²(Ω))-error estimates for the rele- vant variables. Numerical results are presented to support the theory developed in this paper.
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참고문헌 (25)
참고문헌 신청
A. Ern / 2004 / Theory and Practice of Finite Elements / Springer-Verlag
C. Bi / 2007 / Two-grid finite volume element method for linear and nonlinear elliptic problems / Numer. Math 108 (2) : 177 ~ 198
C. Chen / 1989 / Error estimates of optimal order for finite element methods with interpolated coefficients for the nonlinear heat equation / IMA J. Numer. Anal 9 (4) : 507 ~
C. Dawson / 1994 / Two-grid methods for mixed finite element approximations of nonlinear parabolic equations, Domain decomposition methods in scientific and engineering computing / Amer
D. Kim / 2007 / A posteriori error estimator for expanded mixed hybrid methods / Numer. Methods Partial Differential Equations 23 (2) : 330 ~ 349
C. Bi / 2007 / Two-grid finite volume element method for linear and nonlinear elliptic problems / Numer. Math 108 (2) : 177 ~ 198
C. Chen / 1989 / Error estimates of optimal order for finite element methods with interpolated coefficients for the nonlinear heat equation / IMA J. Numer. Anal 9 (4) : 507 ~
C. Dawson / 1994 / Two-grid methods for mixed finite element approximations of nonlinear parabolic equations, Domain decomposition methods in scientific and engineering computing / Amer
D. Kim / 2007 / A posteriori error estimator for expanded mixed hybrid methods / Numer. Methods Partial Differential Equations 23 (2) : 330 ~ 349
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