An EDG Method for Distributed Optimal Control of Elliptic PDEs
arXiv:1801.029785 citationsh-index: 16
Originality Synthesis-oriented
AI Analysis
Provides a new numerical method for solving PDE-constrained optimization problems, but the contribution is incremental as it applies existing EDG techniques to a known problem class.
Proposed an embedded discontinuous Galerkin method for distributed optimal control of elliptic PDEs, deriving optimal error estimates for state, dual state, and control, with numerical validation.
We consider a distributed optimal control problem governed by an elliptic PDE, and propose an embedded discontinuous Galerkin (EDG) method to approximate the solution. We derive optimal a priori error estimates for the state, dual state, the optimal control, and suboptimal estimates for the fluxes. We present numerical experiments to confirm our theoretical results.