3 papers
cs.LG2026
ELADO: Elliptic PDE Assessment Datasets for Operator Learning
Frank Ehebrecht, Toni Scharle, Martin Atzmueller
We introduce ELADO (Elliptic PDE Assessment Datasets for Operator Learning), a systematic benchmark suite constructed to show and quantify failure modes of neural operator architec…
math.NA2020
Uniform Hölder-norm bounds for finite element approximations of second-order elliptic equations
Lars Diening, Toni Scharle, Endre Süli
We develop a discrete counterpart of the De Giorgi-Nash-Moser theory, which provides uniform Hölder-norm bounds on continuous piecewise affine finite element approximations of seco…
math.AP2016
The local boundedness of gradients of weak solutions to elliptic and parabolic phi-Laplacian systems
Toni Scharle
In this thesis, a unified approach to prove the boundedness of gradients of solutions to degenerate and singular elliptic and parabolic phi-Laplacian systems is presented. At first…