On using the cell discretization algorithm for mixed-boundary value problems and domain decomposition (Q1971851)

This paper deals with the approximate solutions to selfadjoint elliptic equations with general nonhomogeneous Dirichlet or Neumann or mixed boundary values. Domains are partitioned into cells and approximations on each cell are constructed using any basis. Another set of basis functions defined on the interfaces between cells is used to achieve weak continuity on the entire domain by requiring that the differences of the traces of approximations on the common boundaries of adjacent cells be orthogonal to increasing numbers of the interface basis a process called moment collocation. Error estimates to establish convergence of the approximations are presented. The author considers a problem with relatively large cells and tests two different domain decompositions. He uses a 10th degree polynomials basis for approximations, with a 7th or 8th degree Legendre polynomial basis employed for interface collocation. m7.