Journal
JOURNAL OF SCIENTIFIC COMPUTING
Volume 71, Issue 3, Pages 897-918Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-016-0325-3
Keywords
Weak Galerkin; Finite element methods; Fourth order problem; Weak second order elliptic operator; Fluorescence tomography; Polygonal or polyhedral meshes
Categories
Funding
- National Science Foundation [DMS-1522586, DMS-1620345, DMS-1042998, DMS-1419027]
- Office of Naval Research [N000141310408]
- National Natural Science Foundation of China [11526113]
- Jiangsu Key Lab for NSLSCS [201602]
- Jiangsu Provincial Foundation Award [BK20050538]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1620345] Funding Source: National Science Foundation
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In this paper, an innovative and effective numerical algorithm by the use of weak Galerkin (WG) finite element methods is proposed for a type of fourth order problem arising from fluorescence tomography. Fluorescence tomography is emerging as an in vivo non-invasive 3D imaging technique reconstructing images that characterize the distribution of molecules tagged by fluorophores. Weak second order elliptic operator and its discrete version are introduced for a class of discontinuous functions defined on a finite element partition of the domain consisting of general polygons or polyhedra. An error estimate of optimal order is derived in an H-kappa(2)-equivalent norm for the WG finite element solutions. Error estimates of optimal order except the lowest order finite element in the usual L-2 norm are established for the WG finite element approximations. Numerical tests are presented to demonstrate the accuracy and efficiency of the theory established for the WG numerical algorithm.
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