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Discretization errors at free boundaries of the Grad-Schlüter-Shafranov equation. (English) Zbl 0712.65110
Numer. Math. (to appear).
The numerical error of standard finite-difference schemes is analyzed at free boundaries of the Grad-Schlüter-Shafranov equation of plasma physics. A simple correction strategy is devised to eliminate (to leading order) the errors which arise as the free boundary crosses the rectangular grid at irregular locations. The resulting scheme can be solved by Gauss-Newton or inverse iterations, or by multigrid iterations. Extrapolation (from 2nd to 3rd order of accuracy) is possible for the new scheme.
Reviewer: R.Meyer-Spasche

MSC:
65Z05 Applications to the sciences
65N15 Error bounds for boundary value problems involving PDEs
35R35 Free boundary problems for PDEs
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
35Q35 PDEs in connection with fluid mechanics
35J60 Nonlinear elliptic equations
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