Computer Methods in Applied Mechanics and Engineering - Special edition on the 20th Anniversary
Stabilized finite element methods. I: Application to the advective-diffusive model
Computer Methods in Applied Mechanics and Engineering
What are C and h?: inequalities for the analysis and design of finite element methods
Computer Methods in Applied Mechanics and Engineering
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Integrated space-time adaptive hp-refinement methods for parabolic systems
Applied Numerical Mathematics
High-order finite element methods for singularly perturbed elliptic and parabolic problems
SIAM Journal on Applied Mathematics
Adaptive mesh refinement for singular current sheets in incompressible magnetohydrodynamic flows
Journal of Computational Physics
Journal of Computational Physics
An adaptive finite element method for magnetohydrodynamics
Journal of Computational Physics
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
A triangular finite element with first-derivative continuity applied to fusion MHD applications
Journal of Computational Physics
Implicit adaptive mesh refinement for 2D reduced resistive magnetohydrodynamics
Journal of Computational Physics
Towards a scalable fully-implicit fully-coupled resistive MHD formulation with stabilized FE methods
Journal of Computational Physics
Hi-index | 31.46 |
We describe a procedure for the adaptive h-refinement solution of the incompressible MHD equations in stream function form using a stabilized finite element formulation. The mesh is adapted based on a posteriori spatial error estimates of the magnetic field using both recovery and order extrapolation techniques. The step size for time integration is chosen so that temporal discretization errors are small relative to spatial errors. The adaptive procedure is applied to study singular current sheets in the tilt instability problem of ideal magnetohydrodynamics. Numerical results indicate a more accurate resolution of current sheets with higher-order methods than with piecewise-linear approximations.