Abstract
In this article, we study a finite element approximation for a model free boundary plasma problem. Using a mixed approach (which resembles an optimal control problem with control constraints), we formulate a weak formulation and study the existence and uniqueness of a solution to the continuous model problem. Using the same setting, we formulate and analyze the discrete problem. We derive optimal order energy norm a priori error estimates proving the convergence of the method. Further, we derive a reliable and efficient a posteriori error estimator for the adaptive mesh refinement algorithm. Finally, we illustrate the theoretical results by some numerical examples.
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Communicated by: Jan Hesthaven
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Cui, J., Gudi, T. Finite element approximation of a free boundary plasma problem. Adv Comput Math 43, 517–535 (2017). https://doi.org/10.1007/s10444-016-9495-7
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DOI: https://doi.org/10.1007/s10444-016-9495-7