LOW REGULARITY PRIMAL-DUAL WEAK GALERKIN FINITE ELEMENT METHODS FOR ILL-POSED ELLIPTIC CAUCHY PROBLEMS

Chunmei Wang

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)33-51
Number of pages19
JournalInternational Journal of Numerical Analysis and Modeling
Volume19
Issue number1
StatePublished - 2022

Keywords

  • Elliptic Cauchy equations
  • Finite element method
  • Ill-posed
  • Low regularity
  • Primal-dual
  • Weak Galerkin

Fingerprint

Dive into the research topics of 'LOW REGULARITY PRIMAL-DUAL WEAK GALERKIN FINITE ELEMENT METHODS FOR ILL-POSED ELLIPTIC CAUCHY PROBLEMS'. Together they form a unique fingerprint.

Cite this