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Guaranteed stability bounds for second-order PDE problems satisfying a Garding inequality
arXiv:2601.00404v1 Announce Type: new
Abstract: We propose an algorithm to numerically determined whether a second-order linear PDE problem satisfying a Garding inequality is well-posed. This algorithm further provides a lower bound to the inf-sup constant of the weak formulation, which may in turn be used for a posteriori error estimation purposes. Our numerical lower bound is based on two discrete singular value problems involving a Lagrange finite element discretization coupled with an a posteriori error estimator based on flux reconstruction techniques. We show that if the finite element discretization is sufficiently rich, our lower bound underestimates the optimal constant only by a factor roughly equal to two.
Abstract: We propose an algorithm to numerically determined whether a second-order linear PDE problem satisfying a Garding inequality is well-posed. This algorithm further provides a lower bound to the inf-sup constant of the weak formulation, which may in turn be used for a posteriori error estimation purposes. Our numerical lower bound is based on two discrete singular value problems involving a Lagrange finite element discretization coupled with an a posteriori error estimator based on flux reconstruction techniques. We show that if the finite element discretization is sufficiently rich, our lower bound underestimates the optimal constant only by a factor roughly equal to two.
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