TY - JOUR
T1 - A new primal-dual weak Galerkin finite element method for ill-posed elliptic Cauchy problems
AU - Wang, Chunmei
N1 - Publisher Copyright:
© 2019 Elsevier B.V.
PY - 2020/6
Y1 - 2020/6
N2 - 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 L2 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.
AB - 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 L2 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.
KW - Elliptic Cauchy problem
KW - Finite element methods
KW - Polygonal or polyhedral meshes
KW - Primal–dual
KW - Weak Galerkin
KW - Weak gradient
UR - http://www.scopus.com/inward/record.url?scp=85076218556&partnerID=8YFLogxK
U2 - 10.1016/j.cam.2019.112629
DO - 10.1016/j.cam.2019.112629
M3 - Article
AN - SCOPUS:85076218556
SN - 0377-0427
VL - 371
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
M1 - 112629
ER -