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.
Original language | English |
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Pages (from-to) | 33-51 |
Number of pages | 19 |
Journal | International Journal of Numerical Analysis and Modeling |
Volume | 19 |
Issue number | 1 |
State | Published - 2022 |
Keywords
- Elliptic Cauchy equations
- Finite element method
- Ill-posed
- Low regularity
- Primal-dual
- Weak Galerkin