TY - JOUR
T1 - A Weak Galerkin Finite Element Method for a Type of Fourth Order Problem Arising from Fluorescence Tomography
AU - Wang, Chunmei
AU - Zhou, Haomin
N1 - Funding Information:
The research of Chunmei Wang was partially supported by National Science Foundation Award DMS-1522586, National Natural Science Foundation of China Award #11526113, Jiangsu Key Lab for NSLSCS Grant #201602, and by Jiangsu Provincial Foundation Award #BK20050538.
Funding Information:
Funding was provided by National Science Foundation (Grant Nos. DMS-1522586, DMS-1620345, DMS-1042998, DMS-1419027), Office of Naval Research (Grant No. N000141310408), National Natural Science Foundation of China (Grant No. 11526113), Jiangsu Key Lab for NSLSCS (Grant No. 201602), and by Jiangsu Provincial Foundation Award (No. BK20050538).
Funding Information:
The research of Haomin Zhou was supported by NSF Faculty Early Career Development(CAREER) Award DMS-1620345, DMS-1042998, DMS-1419027, and ONR Award N000141310408.
Publisher Copyright:
© 2016, Springer Science+Business Media New York.
PY - 2017/6/1
Y1 - 2017/6/1
N2 - 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 Hκ2-equivalent norm for the WG finite element solutions. Error estimates of optimal order except the lowest order finite element in the usual L2 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.
AB - 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 Hκ2-equivalent norm for the WG finite element solutions. Error estimates of optimal order except the lowest order finite element in the usual L2 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.
KW - Finite element methods
KW - Fluorescence tomography
KW - Fourth order problem
KW - Polygonal or polyhedral meshes
KW - Weak Galerkin
KW - Weak second order elliptic operator
UR - http://www.scopus.com/inward/record.url?scp=84996549802&partnerID=8YFLogxK
U2 - 10.1007/s10915-016-0325-3
DO - 10.1007/s10915-016-0325-3
M3 - Article
AN - SCOPUS:84996549802
VL - 71
SP - 897
EP - 918
JO - Journal of Scientific Computing
JF - Journal of Scientific Computing
SN - 0885-7474
IS - 3
ER -