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Volume 19, Issue 1
L​ow Regularity Primal-Dual Weak Galerkin Finite Element Methods for Ill-Posed Elliptic Cauchy Problems

Chunmei Wang

Int. J. Numer. Anal. Mod., 19 (2022), pp. 33-51.

Published online: 2022-03

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  • Abstract

A new primal-dual weak Galerkin (PDWG) finite element method is introduced and analyzed for the ill-posed elliptic Cauchy problems with ultra-low regularity assumptions on the exact solution. The Euler-Lagrange formulation resulting from the PDWG scheme yields a system of equations involving both the primal equation and the adjoint (dual) equation. The optimal order error estimate for the primal variable in a low regularity assumption is established. A series of numerical experiments are illustrated to validate effectiveness of the developed theory.

  • Keywords

Primal-dual, finite element method, weak Galerkin, low regularity, elliptic Cauchy equations, ill-posed.

  • AMS Subject Headings

65N30, 65N12, 35J15, 35D35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-19-33, author = {Wang , Chunmei}, title = {L​ow Regularity Primal-Dual Weak Galerkin Finite Element Methods for Ill-Posed Elliptic Cauchy Problems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2022}, volume = {19}, number = {1}, pages = {33--51}, abstract = {

A new primal-dual weak Galerkin (PDWG) finite element method is introduced and analyzed for the ill-posed elliptic Cauchy problems with ultra-low regularity assumptions on the exact solution. The Euler-Lagrange formulation resulting from the PDWG scheme yields a system of equations involving both the primal equation and the adjoint (dual) equation. The optimal order error estimate for the primal variable in a low regularity assumption is established. A series of numerical experiments are illustrated to validate effectiveness of the developed theory.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/20348.html} }
TY - JOUR T1 - L​ow Regularity Primal-Dual Weak Galerkin Finite Element Methods for Ill-Posed Elliptic Cauchy Problems AU - Wang , Chunmei JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 33 EP - 51 PY - 2022 DA - 2022/03 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/20348.html KW - Primal-dual, finite element method, weak Galerkin, low regularity, elliptic Cauchy equations, ill-posed. AB -

A new primal-dual weak Galerkin (PDWG) finite element method is introduced and analyzed for the ill-posed elliptic Cauchy problems with ultra-low regularity assumptions on the exact solution. The Euler-Lagrange formulation resulting from the PDWG scheme yields a system of equations involving both the primal equation and the adjoint (dual) equation. The optimal order error estimate for the primal variable in a low regularity assumption is established. A series of numerical experiments are illustrated to validate effectiveness of the developed theory.

Chunmei Wang. (2022). L​ow Regularity Primal-Dual Weak Galerkin Finite Element Methods for Ill-Posed Elliptic Cauchy Problems. International Journal of Numerical Analysis and Modeling. 19 (1). 33-51. doi:
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