BPX‐type Preconditioners for Second and Fourth Order Elliptic Problems on the Sphere | Zendy

Jan Maes | Zendy; Angela Kunoth | Zendy; Adhemar Bultheel | Zendy

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BPX‐type Preconditioners for Second and Fourth Order Elliptic Problems on the Sphere

Author(s) -

Jan Maes,

Angela Kunoth,

Adhemar Bultheel

Publication year - 2007

Publication title -

siam journal on numerical analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.78

H-Index - 134

eISSN - 1095-7170

pISSN - 0036-1429

DOI - 10.1137/050647414

Subject(s) - mathematics , discretization , type (biology) , order (exchange) , basis (linear algebra) , mathematical analysis , geometry , ecology , finance , economics , biology

We develop two Bramble-Pasciak-Xu-type preconditioners for second resp. fourth order elliptic problems on the surface of the two-sphere. To discretize the second order problem we use C^0 linear elements on the sphere, and for the fourth order problem we use C^1 finite elements of Powell-Sabin type on the sphere. The main idea why these BPX preconditioners work depends on this particular choice of basis. We prove optimality and provide numerical examples. Furthermore we numerically compare the BPX preconditioners with the suboptimal hierarchical basis preconditioners.status: publishe

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