具有变系数四阶抛物方程的B样条有限元法

Abstract

Abstract: We used the cubic B-spline finite element method to solve a class of fourth order parabolic equations with variable coefficient, and proved the boundness and convergence of the solution of the semi-discrete scheme. For the discretization of time variable, the backward Euler scheme was
constructed, and the convergence order of the solution of the fully discrete scheme was O(Δt+h⁴). A numerical experiment verified the effectiveness of theoretical analysis results and the B-spline finite element method.

Key words: variable coefficient, fourth order parabolic equation, B-spline, finite element method

CLC Number:

O241.82

QIN Dandan, TANG Xinxin, HUANG Wenzhu. B-Spline Finite Element Method for Fourth Order Parabolic Equations with Variable Coefficient[J].Journal of Jilin University Science Edition, 2020, 58(5): 1100-1106.

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B-Spline Finite Element Method for Fourth Order Parabolic Equations with Variable Coefficient

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