The authors derive rigorous a posteriori error bounds in the L^∞(L²) norm for an arbitrary-order space-time FEM for the wave equation that supports adaptive mesh modification via temporal reconstructions.
Verfürth.A Posteriori Error Estimation Techniques for Finite Element Methods
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A posteriori error analysis and adaptivity of a space-time finite element method for the wave equation in second order formulation
The authors derive rigorous a posteriori error bounds in the L^∞(L²) norm for an arbitrary-order space-time FEM for the wave equation that supports adaptive mesh modification via temporal reconstructions.