Splitting extrapolation based on domain decomposition for finite element approximations
The authors study a method called splitting extrapolation which is meant to be a competitive algorithm for large scale problems. Advantages of domain decomposition and sparse-grid methods are combined with high accuracy. The method applies to elliptic second-order problems, linear and nonlinear, and eigenvalue problems, in two and three space dimensions. Large scale problems are decomposed into many smaller discrete problems which can be solved in parallel. Multivariate asymptotic expansions of finite element errors are exploited. In Section 1 three theorems -- one for each type of problem -- are formulated, giving the form of the expansion. Sections 2 through 4 contain the proofs. Sections 5 and 6 contain details of the algorithm and examples in three dimensions with known analytical solutions.
scientific article; zbMATH DE number 1066763