A priori error analysis of a stabilized finite-element scheme for an elliptic equation with time-dependent boundary conditions
Jmeih N. Abou, Arwadi T. El, S. Dib
Beirut Arab University, Beirut, Lebanon
Keywords: finite element scheme, a priori error analysis, dynamical boundary conditions, Dirichlet-to-Neumann semigroup
Abstract
This study aims to implement a numerical scheme in order to find the eigenvalues of the Dirichlet-to-Neumann semigroup. This can be used to check its positivity for non-circular domains. This generalized scheme is analyzed after studying the case of the unit ball, in which an explicit representation for the semigroup was obtained by Peter Lax. After analyzing the generalized scheme, we checked its convergence through numerical simulations that were performed using FreeFem++ software.
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