Guaranteed inf-sup bounds and existence verification for semilinear elliptic problems via nonconforming finite elements
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910160675405824 |
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| author | Gräßle, Benedikt |
| author_facet | Gräßle, Benedikt |
| contents | A Newton--Kantorovich-type argument enables the a posteriori existence verification of a unique regular root near a computed approximation, purely from computable data. This framework allows for non-selfadjoint problems and extends the existing verification theory to nonconforming discretisations. A key ingredient is a guaranteed lower bound on the continuous inf-sup constant from a quasi-optimal nonconforming discretisation that enables a novel a priori error estimator. All quantities are obtained by post-processing a single discretisation; convergence rates are proved. The theory is applied to a fourth-order formulation of the stationary two-dimensional Navier--Stokes equations and illustrated by numerical experiments. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_21887 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Guaranteed inf-sup bounds and existence verification for semilinear elliptic problems via nonconforming finite elements Gräßle, Benedikt Numerical Analysis 65N30, 65N12, 65N50 A Newton--Kantorovich-type argument enables the a posteriori existence verification of a unique regular root near a computed approximation, purely from computable data. This framework allows for non-selfadjoint problems and extends the existing verification theory to nonconforming discretisations. A key ingredient is a guaranteed lower bound on the continuous inf-sup constant from a quasi-optimal nonconforming discretisation that enables a novel a priori error estimator. All quantities are obtained by post-processing a single discretisation; convergence rates are proved. The theory is applied to a fourth-order formulation of the stationary two-dimensional Navier--Stokes equations and illustrated by numerical experiments. |
| title | Guaranteed inf-sup bounds and existence verification for semilinear elliptic problems via nonconforming finite elements |
| topic | Numerical Analysis 65N30, 65N12, 65N50 |
| url | https://arxiv.org/abs/2604.21887 |