Browsing by Author "Cowsar, Lawrence C."

Now showing 1 - 3 of 3
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    Domain Decomposition Methods for Nonconforming Finite Element Spaces of Lagrange-Type
    (1993-03) Cowsar, Lawrence C.
    In this article, we consider the application of three popular domain decomposition methods to Lagrange-type nonconforming finite element discretizations of scalar, self-adjoint, second order elliptic equations. The additive Schwarz method of Dryja and Widlund, the vertex space method of Smith, and the balancing method of Mandel applied to nonconforming elements are shown to converge at the same rate as their applications to the standard conforming piecewise linear Galerkin discretization. Essentially, the theory for the nonconforming elements is inherited from the existing theory for the conforming elements with only modest modification by constructing an isomorphism between the nonconforming finite element space and a space of continuous piecewise linear functions.
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    Dual-Variable Schwarz Methods for Mixed Finite Elements
    (1993-03) Cowsar, Lawrence C.
    Schwarz methods for the mixed finite element discretization of second order elliptic problems are considered. By using an equivalence between mixed methods and conforming spaces first introduced in [13], it is shown that the condition number of the standard additive Schwarz method applied to the dual-variable system grows at worst like O(1+H/delta) in both two and three dimensions and for elements of any order. Here, H is the size of the subdomains, and delta is a measure of the overlap. Numerical results are presented that verify the bound.
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    Parallel Domain Decomposition Method for Mixed Finite Elements for Elliptic Partial Differential Equations
    (1990-11) Cowsar, Lawrence C.; Wheeler, Mary F.
    In this paper we develop a parallel domain decomposition method for mixed finite element methods. This algorithm is based on a procedure first formulated by Glowinski and Wheeler for a two subdomain problem. This present work involves extensions of the above method to an arbitrary number of subdomains with an inner product modification and multilevel acceleration. Both Neumann and Dirichlet boundary conditions are treated. Numerical experiments performed on the Intel iPSC/860 Hypercube are presented and indicate that this approach is scalable and fairly insensitive to variation in coefficients.