20.500.12556/RUP-21388 A ▫$C^s$▫-smooth mixed degree and regularity isogeometric spline space over planar multi-patch domains We construct over a given bilinear multi-patch domain a novel $C^s$-smooth mixed degree and regularity isogeometric spline space, which possesses the degree $p=2s+1$ and regularity $r=s$ in a small neighborhood around the edges and vertices, and the degree~$\widetilde{p} \leq p$ with regularity $\widetilde{r} = \widetilde{p}-1 \geq r$ in all other parts of the domain. Our proposed approach relies on the technique Kapl and Vitrih (2021), which requires for the $C^s$-smooth isogeometric spline space a degree at least $p=2s+1$ on the entire multi-patch domain. Similar to Kapl and Vitrih (2021), the $C^s$-smooth mixed degree and regularity spline space is generated as the span of basis functions that correspond to the individual patches, edges and vertices of the domain. The reduction of degrees of freedom for the functions in the interior of the patches is achieved by introducing an appropriate mixed degree and regularity underlying spline space over $[0,1]^2$ to define the functions on the single patches. We further extend our construction with a few examples to the class of bilinear-like $G^8$ multi-patch parameterizations (Kapl and Vitrih (2018); Kapl and Vitrih (2021)), which enables the design of multi-patch domains having curved boundaries and interfaces. Finally, the great potential of the $C^8$-smooth mixed degree and regularity isogeometric spline space for performing isogeometric analysis is demonstrated by several numerical examples of solving two particular high order partial differential equations, namely the biharmonic and triharmonic equation, via the isogeometric Galerkin method. isogeometric analysis Galerkin method C^s-smoothness mixed degree and regularity spline space multi-patch domain izogeometrična analiza Galerkinova metoda C^s-gladkost prostor zlepkov mešanih stopenj in regularnosti večdelne domene true false false Angleški jezik Slovenski jezik Članek v reviji 2025-07-01 10:08:55 2025-07-01 10:08:56 2025-07-02 03:04:52 0000-00-00 00:00:00 2026 0 0 str. 1-21 [article no.] 116836 Vol. 473 Feb. 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2025-06-17 519.65 0377-0427 10.1016/j.cam.2025.116836 240913667 RAZ_Kapl_Mario_2026.pdf RAZ_Kapl_Mario_2026.pdf 1 E3279613C2560D1FCAF28CB94E89C5F5 d0f5cc0ae5cdb119584fb885591933253d52dc802665dca3674f88ad98c86e24 b8e845e1-5652-11f0-bc14-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=31118 https://www.sciencedirect.com/science/article/pii/S0377042725003504?via%3Dihub 1 8c4142d4-5652-11f0-bc14-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=31117 Fakulteta za matematiko, naravoslovje in informacijske tehnologije 0 0 0