Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 371, Issue -, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.cam.2019.112629
Keywords
Primal-dual; Weak Galerkin; Finite element methods; Elliptic Cauchy problem; Weak gradient; Polygonal or polyhedral meshes
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Funding
- National Science Foundation [DMS-1849483]
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A new numerical method is devised and analyzed for a type of ill-posed elliptic Cauchy problems by using the primal-dual weak Galerkin finite element method. This new primal-dual weak Galerkin algorithm is robust and efficient in the sense that the system arising from the scheme is symmetric, well-posed, and is satisfied by the exact solution (if it exists). An error estimate of optimal order is established for the corresponding numerical solutions in a scaled residual norm. In addition, a mathematical convergence is established in a weak L-2 topology for the new numerical method. Numerical results are reported to demonstrate the efficiency of the primal-dual weak Galerkin method as well as the accuracy of the numerical approximations. (C) 2019 Elsevier B.V. All rights reserved.
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