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arXiv · 1809.04697

A New Primal-Dual Weak Galerkin Finite Element Method for Ill-posed Elliptic Cauchy Problems

Chunmei Wang
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Abstract

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.

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Chunmei Wang. 2018-09-12. A New Primal-Dual Weak Galerkin Finite Element Method for Ill-posed Elliptic Cauchy Problems. https://arxiv.org/abs/1809.04697

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