FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2898980015> ?p ?o ?g. }

• W2898980015 abstract "In this paper, we study the mathematical structure and numerical approximation of elliptic problems posed in a (3D) domain $Omega$ when the right-hand side is a (1D) line source $Lambda$. The analysis and approximation of such problems is known to be non-standard as the line source causes the solution to be singular. Our main result is a splitting theorem for the solution; we show that the solution admits a split into an explicit, low regularity term capturing the singularity, and a high-regularity correction term $w$ being the solution of a suitable elliptic equation. The splitting theorem states the mathematical structure of the solution; in particular, we find that the solution has anisotropic regularity. More precisely, the solution fails to belong to $H^1$ in the neighbourhood of $Lambda$, but exhibits piecewise $H^2$-regularity parallel to $Lambda$. The splitting theorem can further be used to formulate a numerical method in which the solution is approximated via its correction function $w$. This approach has several benefits. Firstly, it recasts the problem as a 3D elliptic problem with a 3D right-hand side belonging to $L^2$, a problem for which the discretizations and solvers are readily available. Secondly, it makes the numerical approximation independent of the discretization of $Lambda$; thirdly, it improves the approximation properties of the numerical method. We consider here the Galerkin finite element method, and show that the singularity subtraction then recovers optimal convergence rates on uniform meshes, i.e., without needing to refine the mesh around each line segment. The numerical method presented in this paper is therefore well-suited for applications involving a large number of line segments. We illustrate this by treating a dataset (consisting of $sim 3000$ line segments) describing the vascular system of the brain." @default.
• W2898980015 created "2018-11-09" @default.
• W2898980015 creator A5003279094 @default.
• W2898980015 creator A5018841476 @default.
• W2898980015 creator A5084832937 @default.
• W2898980015 creator A5087384117 @default.
• W2898980015 date "2018-10-30" @default.
• W2898980015 modified "2023-09-27" @default.
• W2898980015 title "Splitting method for elliptic equations with line sources." @default.
• W2898980015 cites W1168767242 @default.
• W2898980015 cites W130356082 @default.
• W2898980015 cites W1537887709 @default.
• W2898980015 cites W1569090332 @default.
• W2898980015 cites W1573339040 @default.
• W2898980015 cites W1977419424 @default.
• W2898980015 cites W1979022019 @default.
• W2898980015 cites W1984320368 @default.
• W2898980015 cites W2001032894 @default.
• W2898980015 cites W2011662851 @default.
• W2898980015 cites W2030604754 @default.
• W2898980015 cites W2039277388 @default.
• W2898980015 cites W2040299291 @default.
• W2898980015 cites W2056609036 @default.
• W2898980015 cites W2062341308 @default.
• W2898980015 cites W2073216552 @default.
• W2898980015 cites W2078434021 @default.
• W2898980015 cites W2094293004 @default.
• W2898980015 cites W2139528660 @default.
• W2898980015 cites W2168060295 @default.
• W2898980015 cites W2470472984 @default.
• W2898980015 cites W2518693057 @default.
• W2898980015 cites W2522238075 @default.
• W2898980015 cites W2528558002 @default.
• W2898980015 cites W2554554440 @default.
• W2898980015 cites W2595548973 @default.
• W2898980015 cites W2752065194 @default.
• W2898980015 cites W2788153039 @default.
• W2898980015 cites W2888073692 @default.
• W2898980015 cites W2901074353 @default.
• W2898980015 cites W3021722416 @default.
• W2898980015 cites W3099792816 @default.
• W2898980015 cites W3104566386 @default.
• W2898980015 cites W73123583 @default.
• W2898980015 cites W90568776 @default.
• W2898980015 hasPublicationYear "2018" @default.
• W2898980015 type Work @default.
• W2898980015 sameAs 2898980015 @default.
• W2898980015 citedByCount "4" @default.
• W2898980015 countsByYear W28989800152018 @default.
• W2898980015 countsByYear W28989800152019 @default.
• W2898980015 countsByYear W28989800152020 @default.
• W2898980015 crossrefType "posted-content" @default.
• W2898980015 hasAuthorship W2898980015A5003279094 @default.
• W2898980015 hasAuthorship W2898980015A5018841476 @default.
• W2898980015 hasAuthorship W2898980015A5084832937 @default.
• W2898980015 hasAuthorship W2898980015A5087384117 @default.
• W2898980015 hasConcept C121332964 @default.
• W2898980015 hasConcept C134306372 @default.
• W2898980015 hasConcept C135628077 @default.
• W2898980015 hasConcept C16171025 @default.
• W2898980015 hasConcept C164660894 @default.
• W2898980015 hasConcept C179603306 @default.
• W2898980015 hasConcept C2524010 @default.
• W2898980015 hasConcept C28826006 @default.
• W2898980015 hasConcept C31487907 @default.
• W2898980015 hasConcept C33923547 @default.
• W2898980015 hasConcept C48753275 @default.
• W2898980015 hasConcept C73000952 @default.
• W2898980015 hasConcept C97355855 @default.
• W2898980015 hasConceptScore W2898980015C121332964 @default.
• W2898980015 hasConceptScore W2898980015C134306372 @default.
• W2898980015 hasConceptScore W2898980015C135628077 @default.
• W2898980015 hasConceptScore W2898980015C16171025 @default.
• W2898980015 hasConceptScore W2898980015C164660894 @default.
• W2898980015 hasConceptScore W2898980015C179603306 @default.
• W2898980015 hasConceptScore W2898980015C2524010 @default.
• W2898980015 hasConceptScore W2898980015C28826006 @default.
• W2898980015 hasConceptScore W2898980015C31487907 @default.
• W2898980015 hasConceptScore W2898980015C33923547 @default.
• W2898980015 hasConceptScore W2898980015C48753275 @default.
• W2898980015 hasConceptScore W2898980015C73000952 @default.
• W2898980015 hasConceptScore W2898980015C97355855 @default.
• W2898980015 hasLocation W28989800151 @default.
• W2898980015 hasOpenAccess W2898980015 @default.
• W2898980015 hasPrimaryLocation W28989800151 @default.
• W2898980015 hasRelatedWork W1973336426 @default.
• W2898980015 hasRelatedWork W2403626840 @default.
• W2898980015 hasRelatedWork W2745346367 @default.
• W2898980015 hasRelatedWork W2961200669 @default.
• W2898980015 hasRelatedWork W2962925224 @default.
• W2898980015 hasRelatedWork W2988049787 @default.
• W2898980015 hasRelatedWork W2990742369 @default.
• W2898980015 hasRelatedWork W2992880912 @default.
• W2898980015 hasRelatedWork W3018934365 @default.
• W2898980015 hasRelatedWork W3036858476 @default.
• W2898980015 hasRelatedWork W3083002399 @default.
• W2898980015 hasRelatedWork W3161286888 @default.
• W2898980015 hasRelatedWork W3187635229 @default.
• W2898980015 hasRelatedWork W3195892799 @default.
• W2898980015 isParatext "false" @default.

• next