Approximation by finite element method of the model plasma problem. (English) Zbl 0712.76069

Summary: We analyze finite element approximations of the model plasma problem \(- \Delta w=\lambda (w-d)^+\) in \(\Omega\), \(w=0\) on \(\partial \Omega\), \(\lambda\int_{\Omega}(w-d)^+dx=j\), where \(\Omega\) is a bounded domain in \({\mathbb{R}}^ 2\) with boundary \(\partial \Omega\) and j is a given positive number; the function w and the real number \(\lambda\) are the unknowns, d is a parameter. We can show that the finite element approximation, in the case of numerical integration too, converges in the norms of \(H^ 1(\Omega)\) and \(L^{\infty}(\Omega)\) at the optimal rate.


76M10 Finite element methods applied to problems in fluid mechanics
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
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