A Weak Galerkin Finite Element Method for a Type of Fourth Order Problem Arising from Fluorescence Tomography

作者：Wang Chunmei^*; Zhou Haomin

来源：Journal of Scientific Computing, 2017, 71(3): 897-918.

DOI：10.1007/s10915-016-0325-3

• Weak Galerkin
• Finite element methods
• Fourth order problem
• Weak second order elliptic operator
• Fluorescence tomography
• Polygonal or polyhedral meshes

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.

• 出版日期2017-6