Estimating and localizing the algebraic and total errors

Main results: total, algebraic, and discretization errors: guaranteed upper and lower bounds; valid for arbitrary iterative algebraic solver; estimating the local distribution of the errors over the computational domain; safe stopping criteria for iterative algebraic solvers: the algebraic error will lie below the discretization one. Details: paper (preprint) with Jan…

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Stopping criteria for domain decomposition methods

Main results: guaranteed error upper bound on each DD iteration; distinguishes the domain decomposition error, the spatial discretization error, and possibly the temporal discretization error; important savings in terms of the number of domain decomposition iterations; optimized Robin and Ventcell transmission conditions; global-in-time formulation that allows for use of local…

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Potential and flux reconstructions a posteriori error estimates

Main results: potential and equilibrated flux reconstruction estimates in a unified framework; inhomogeneous Dirichlet and Neumann boundary conditions; spatially varying polynomial degree; mixed rectangular-triangular grids; combination with the H(div)-liftings paper: robustness with respect to the number of hanging nodes; asymptotic exactness observed for smooth solutions; hp-adaptivity strategy numerically leading to…

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