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A filter method with a priori and a posteriori parameter choice for the regularization of Cauchy problems for biharmonic equations

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Abstract

In the present paper, we devote our effort to Cauchy boundary value problems for biharmonic equations. In general, the investigated problem is ill-posed. Therefore, we develop a filter method to defeat the ill-posedness of the problem. Explicit convergence rate is established under both a priori and a posteriori parameter choice rules. Finally, a numerical example is presented to illustrate the ill-posedness of the problem as well as the effectiveness of the proposed method.

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Authors and Affiliations

  1. Institute for Computational Science and Technology, SBI building, Quang Trung Software City, Tan Chanh Hiep Ward, District 12, Ho Chi Minh City, Vietnam

    Tran Nhat Luan & Tran Thi Khieu

  2. Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Tra Quoc Khanh

  3. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Tra Quoc Khanh

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  1. Tran Nhat Luan
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  2. Tran Thi Khieu
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  3. Tra Quoc Khanh
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Correspondence to Tra Quoc Khanh.

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Luan, T.N., Khieu, T.T. & Khanh, T.Q. A filter method with a priori and a posteriori parameter choice for the regularization of Cauchy problems for biharmonic equations. Numer Algor 86, 1721–1746 (2021). https://doi.org/10.1007/s11075-020-00951-4

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  • DOI: https://doi.org/10.1007/s11075-020-00951-4

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