Algebraic multigrid theory: The symmetric case
Applied Mathematics and Computation - Second Copper Mountain conference on Multigrid methods Copper Mountain, Colorado
First-order system least squares for second-order partial differential equations: part I
SIAM Journal on Numerical Analysis - Special issue: the articles in this issue are dedicated to Seymour V. Parter
First-Order System Least Squares for Second-Order Partial Differential Equations: Part II
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
A multigrid tutorial: second edition
A multigrid tutorial: second edition
An implicit, nonlinear reduced resistive MHD solver
Journal of Computational Physics
Analysis of Velocity-Flux Least-Squares Principles for the Navier--Stokes Equations: Part II
SIAM Journal on Numerical Analysis
Multilevel First-Order System Least Squares for Nonlinear Elliptic Partial Differential Equations
SIAM Journal on Numerical Analysis
Improving robustness in multiscale methods
Improving robustness in multiscale methods
SIAM Journal on Scientific Computing
Implicit adaptive mesh refinement for 2D reduced resistive magnetohydrodynamics
Journal of Computational Physics
Efficiency-based local adaptive refinement for fosls finite elements
Efficiency-based local adaptive refinement for fosls finite elements
First-Order System Least Squares for Incompressible Resistive Magnetohydrodynamics
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
First-order system least squares and the energetic variational approach for two-phase flow
Journal of Computational Physics
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This paper describes the use of an efficiency-based adaptive mesh refinement scheme, known as ACE, on a 2D reduced model of the incompressible, resistive magnetohydrodynamic (MHD) equations A first-order system least squares (FOSLS) finite element formulation and algebraic multigrid (AMG) are used in the context of nested iteration The FOSLS a posteriori error estimates allow the nested iteration and ACE algorithms to yield the best accuracy-per-computational-cost The ACE scheme chooses which elements to add when interpolating to finer grids so that the best error reduction with the least amount of cost is obtained, when solving on the refined grid We show that these methods, applied to the simulation of a tokamak fusion reactor instability, yield approximations to solutions within discretization accuracy using less than the equivalent amount of work needed to perform 10 residual calculations on the finest uniform grid.