A Trefftz/MFS mixed-type method to solve the Cauchy problem of the Laplace equation

DOI10.1016/j.aml.2018.07.028zbMath1428.65100OpenAlexW2884637255WikidataQ129439590 ScholiaQ129439590MaRDI QIDQ1726498

Yan Gu, Fajie Wang, Chein-Shan Liu

Publication date: 20 February 2019

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2018.07.028

zbMATH Keywords

Cauchy problemLaplace equationTrefftz methodMFS test functionsmixed-type method

Mathematics Subject Classification ID

Ill-posedness and regularization problems in numerical linear algebra (65F22) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Fundamental solutions to PDEs (35A08) Second-order elliptic equations (35J15) Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs (65N80) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)

Related Items (2)

A homogenization function technique to solve the 3D inverse Cauchy problem of elliptic type equations in a closed walled shell ⋮ Numerical simulation of physical fields by the collocation method

Cites Work

• Unnamed Item
• A modified collocation Trefftz method for the inverse Cauchy problem of Laplace equation
• A modified Tikhonov regularization method for the Cauchy problem of Laplace equation
• A new investigation into regularization techniques for the method of fundamental solutions
• Trefftz energy method for solving the Cauchy problem of the Laplace equation
• Numerical solution of the Laplacian Cauchy problem by using a better postconditioning collocation Trefftz method
• An equilibrated method of fundamental solutions to choose the best source points for the Laplace equation
• The boundary element solution of the Cauchy steady heat conduction problem in an anisotropic medium
• Fourier regularization method for solving a Cauchy problem for the Laplace equation

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