Error estimate of a Legendre-Galerkin Chebyshev collocation method for a class of parabolic inverse problem
Error estimate of a Legendre-Galerkin Chebyshev collocation method for a class of parabolic inverse problem
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DOI：
10.1016/j.apnum.2021.07.023
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发表时间：
2021-12
影响因子：
2.8
通讯作者：
Huiqing Liao;He-ping Ma
中科院分区：
文献类型：
--
作者：
Huiqing Liao;He-ping Ma
摘要对带控制参数的抛物型反问题提出了一种Legendre-Galerkin Chebyshev配置法。当非线性项不是全局Lipschitz连续时，得到了半离散方法在L2范数下的最优收敛阶.对于时间离散化，应用Legendre-tau方法。该方法采用显-隐迭代法实现。构造合适的基函数，导致稀疏矩阵，和非线性项配置在Chebyshev-Gauss-Lobatto点明确计算的快速Legendre变换。数值结果表明，这种时空谱方法的效率和能力。
Abstract A Legendre-Galerkin Chebyshev collocation method is presented for the parabolic inverse problem with control parameters. Optimal order of convergence of the semi-discrete method is obtained in L 2-norm for the nonlinear term being not globally Lipschitz continuous. For time-discretization, a Legendre-tau method is applied. The method is implemented by the explicit-implicit iterative method. Suitable basis functions are constructed leading to sparse matrices, and the nonlinear term is collocated at the Chebyshev-Gauss-Lobatto points computed explicitly by the fast Legendre transform. Numerical results are given to show the efficiency and capability of this space-time spectral method.