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Unconditionally optimal error estimates of a linearized weak Galerkin finite element method for semilinear parabolic equations
Advances in Computational Mathematics ( IF 1.7 ) Pub Date : 2022-07-12 , DOI: 10.1007/s10444-022-09961-3
Ying Liu, Zhen Guan, Yufeng Nie

In this paper, we consider the unconditionally optimal error estimates of the linearized backward Euler scheme with the weak Galerkin finite element method for semilinear parabolic equations. With the error splitting technique and elliptic projection, the optimal error estimates in L2-norm and the discrete H1-norm are derived without any restriction on the time stepsize. Numerical results on both polygonal and tetrahedral meshes are provided to illustrate our theoretical conclusions.



中文翻译:

半线性抛物方程线性化弱Galerkin有限元法的无条件最优误差估计

在本文中,我们考虑了半线性抛物方程的弱 Galerkin 有限元法线性化后向 Euler 格式的无条件最优误差估计。使用误差分裂技术和椭圆投影,得到了L 2范数和离散H 1范数中的最优误差估计,对时间步长没有任何限制。提供了多边形和四面体网格的数值结果来说明我们的理论结论。

更新日期:2022-07-13
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