Analysis of some moving space-time finite element methods
SIAM Journal on Numerical Analysis
The Velocity Tracking Problem for Navier--Stokes Flows with Bounded Distributed Controls
SIAM Journal on Control and Optimization
Journal of Scientific Computing
Optimal Control of Distributed Systems: Theory and Applications
Optimal Control of Distributed Systems: Theory and Applications
Moving mesh methods in multiple dimensions based on harmonic maps
Journal of Computational Physics
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
Symmetric Error Estimates for Moving Mesh Galerkin Methods for Advection-Diffusion Equations
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Adaptive Finite Element Approximation for Distributed Elliptic Optimal Control Problems
SIAM Journal on Control and Optimization
Symmetric Error Estimates for Moving Mesh Mixed Methods for Advection-Diffusion Equations
SIAM Journal on Numerical Analysis
Dynamic-mesh finite element method for Lagrangian computational fluid dynamics
Finite Elements in Analysis and Design - Robert J. Melosh medal competition
Perspectives in Flow Control and Optimization
Perspectives in Flow Control and Optimization
Journal of Computational and Applied Mathematics
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An optimal control problem for the advection-diffusion equation is studied using a Lagrangian-moving mesh finite element method. The weak formulation of the model advection---diffusion equation is based on Lagrangian coordinates, and semi---discrete (in space) error estimates are derived under minimal regularity assumptions. In addition, using these estimates and Brezzi-Rappaz-Raviart theory, symmetric error estimates for the optimality system are derived. The results also apply for advection dominated problems