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.
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Derives fully-discrete a priori and semi-discrete a posteriori error estimates for a C^0-in-time discontinuous-continuous Galerkin discretization of the wave equation, with explicit constants and a C^1 reconstruction operator.
The authors prove existence of optimal controls for a 2D ternary mixture model with evaporation and derive first-order necessary optimality conditions using the adjoint system.
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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.