# Exponential Convergence of hp-Time-Stepping in Space-Time Discretizations of Parabolic PDEs

@article{Perugia2022ExponentialCO, title={Exponential Convergence of hp-Time-Stepping in Space-Time Discretizations of Parabolic PDEs}, author={Ilaria Perugia and Christoph Schwab and Marco Zank}, journal={ArXiv}, year={2022}, volume={abs/2203.11879} }

For linear parabolic initial-boundary value problems with selfadjoint, time-homogeneous elliptic spatial operator in divergence form with Lipschitz-continuous coefficients, and for incompatible, time-analytic forcing term in polygonal/polyhedral domains D, we prove time-analyticity of solutions. Temporal analyticity is quantified in terms of weighted, analytic function classes, for data with finite, low spatial regularity and without boundary compatibility. Leveraging this result, we prove…

## One Citation

Integral Representations and Quadrature Schemes for the Modified Hilbert Transformation

- Mathematics, Computer Science
- 2022

We present quadrature schemes to calculate matrices, where the so-called modiﬁed Hilbert transformation is involved. These matrices occur as temporal parts of Galerkin ﬁnite element discretizations…

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