Abstract
A fully discrete finite element method is proposed for linear wave equations. The spatial discretization is carried out using P l conforming element, while the temporal discretization is obtained using P 1 -continuous discontinuous Galerkin method. Borrowing a novel time reconstruction operator combined with the technique of elliptic reconstruction, a reliable posteriori error bound is developed. Based on this error bound, two adaptive algorithms in time and space separately are proposed. A series of numerical experiments are reported to illustrate the performance of the error bound and the adaptive algorithms proposed.
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