What does this research mean for the field?

Error estimates for Discontinuous Galerkin discretisations of non-linear problems with (p,δ)-structure can be derived under minimal regularity assumptions without oscillation terms. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.CHALLENGES_CONSENSUS.

What question did this study set out to answer?

The aim is to derive error estimates for discontinuous Galerkin discretisations of non-linear Dirichlet problems, with relaxed regularity assumptions.

February 19, 2026Numerische MathematikOpen Access

Quasi-optimal Discontinuous Galerkin discretisations of the p0. 83328pt-Dirichlet problem

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Authors

JBJan BlechtaCharles University PGPablo Alexei Gazca-OrozcoUniversity of Freiburg AKAlex KaltenbachUniversity of Freiburg

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Implication

This research derives error estimates for non-linear Dirichlet problems, implying improved assumptions for solution regularity.

Key Points

The aim is to derive error estimates for discontinuous Galerkin discretisations of non-linear Dirichlet problems, with relaxed regularity assumptions.
Derived error estimates using a smoothing operator.
Focused on non-linear problems with (p,δ)-structure.
Assumed natural W^{1,p}-regularity of the exact solution without oscillation terms.
Established error estimates that only rely on W^{1,p} regularity.
Removed oscillation terms from error estimates allowing for broader solution applications.
Improved upon minimal regularity estimates found in the literature.

Cite This Study

Blechta et al. (2026) studied this question.

synapsesocial.com/papers/6996a8efecb39a600b3f02cb https://doi.org/10.1007/s00211-025-01507-1

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Quasi-optimal Discontinuous Galerkin discretisations of the p0. 83328pt-Dirichlet problem

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Implication

Key Points

Cite This Study

Quasi-optimal Discontinuous Galerkin discretisations of the p0. 83328pt-Dirichlet problem

Discussion

Member takes

Implication

Key Points

Cite This Study

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