A procedure for a posteriori error estimation for h-p finite element methods
Computer Methods in Applied Mechanics and Engineering - Special issue on reliability in computational mechanics
Analysis of least squares finite element methods for the Stokes equations
Mathematics of Computation
Moving finite elements
Mesh Smoothing Using A Posteriori Error Estimates
SIAM Journal on Numerical Analysis
First-Order System Least Squares for the Stokes Equations, with Application to Linear Elasticity
SIAM Journal on Numerical Analysis
A New Moving Mesh Algorithm for the Finite Element Solution of Variational Problems
SIAM Journal on Numerical Analysis
First-Order System Least Squares (FOSLS) for Convection-Diffusion Problems: Numerical Results
SIAM Journal on Scientific Computing
Issues Related to Least-Squares Finite Element Methods for the Stokes Equations
SIAM Journal on Scientific Computing
A multigrid tutorial: second edition
A multigrid tutorial: second edition
First-Order System Least Squares for the Stokes and Linear Elasticity Equations: Further Results
SIAM Journal on Scientific Computing
Adaptive Finite Element Approximation for Distributed Elliptic Optimal Control Problems
SIAM Journal on Control and Optimization
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We describe an algorithm for optimising the mesh in the least-squares finite element discretisation of first-order systems of partial differential equations. The key feature of the method is that the optimisation process is based entirely on the solution of local PDE problems. We apply the algorithm to the Stokes equations for the flow of a viscous incompressible fluid, and to a convection diffusion equation where convection dominates.