Interior maximum-norm estimates for finite element methods, part II
Mathematics of Computation
The full domain partition approach to distributing adaptive grids
Proceedings of international centre for mathematical sciences on Grid adaptation in computational PDES : theory and applications: theory and applications
Local and parallel finite element algorithms for the stokes problem
Numerische Mathematik
Numerical Approximation of Partial Differential Equations
Numerical Approximation of Partial Differential Equations
A new parallel finite element algorithm for the stationary Navier-Stokes equations
Finite Elements in Analysis and Design
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Based on full domain partition, three parallel iterative finite element algorithms for the stationary Navier-Stokes equations are proposed and analyzed. In these algorithms, each subproblem is defined in the entire domain with the vast majority of the degrees of freedom associated with the particular subdomain that it is responsible for and hence can be solved in parallel with other subproblems using an existing sequential solver without extensive recoding. All of the subproblems are nonlinear and are independently solved by three kinds of iterative methods. Under some (strong) uniqueness conditions, errors of the parallel iterative finite element solutions are estimated. Some numerical results are also given which demonstrate the efficiency of the parallel iterative algorithms.