Weak Galerkin Finite Element Methods for Optimal Control Problems Governed by Second Order Elliptic Partial Differential Equations

Chunmei Wang; Junping Wang; Shangyou Zhang

Weak Galerkin Finite Element Methods for Optimal Control Problems Governed by Second Order Elliptic Partial Differential Equations

Numerical Analysis 2023-10-03 v1 Numerical Analysis

Authors: Chunmei Wang , Junping Wang , Shangyou Zhang

Abstract

This paper is concerned with the development of weak Galerkin (WG) finite element method for optimal control problems governed by second order elliptic partial differential equations (PDEs). It is advantageous to use discontinuous finite elements over the traditional $C^1$ finite elements here. Optimal order error estimates are established and confirmed by some numerical tests.

Keywords

weak galerkin finite element methods galerkin methods discontinuous galerkin methods

Cite

@article{arxiv.2310.01373,
  title  = {Weak Galerkin Finite Element Methods for Optimal Control Problems Governed by Second Order Elliptic Partial Differential Equations},
  author = {Chunmei Wang and Junping Wang and Shangyou Zhang},
  journal= {arXiv preprint arXiv:2310.01373},
  year   = {2023}
}

Comments

23 pages, 3 figures, 5 tables. arXiv admin note: substantial text overlap with arXiv:1806.01583

Weak Galerkin Finite Element Methods for Optimal Control Problems Governed by Second Order Elliptic Partial Differential Equations

Abstract

Keywords

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