Analysis of the internodes method for non-conforming discretizations of elliptic equations
نویسندگان
چکیده
INTERNODES is a general method to deal with non-conforming discretizations of second order partial differential equations on regions partitioned into two or several subdomains. It exploits two intergrid interpolation operators, one for transfering the Dirichlet trace across the interface, the others for the Neumann trace. In this paper we provide several interpretations of the method and we carry out its stability and convergence analysis. In every subdomain the original problem is discretized by the finite element method, using a priori non-matching grids and piecewise polynomials of different degree. Finally, we propose an efficient algorithm for the solution of the corresponding algebraic system.
منابع مشابه
Block Jacobi for discontinuous Galerkin discretizations: no ordinary Schwarz methods
For classical discretizations of elliptic partial differential equations, like conforming finite elements or finite differences, block Jacobi methods are equivalent to classical Schwarz methods with minimal overlap, see for example [4]. This is different when the linear system (1) is obtained using DG methods. Our paper is organized as follows: in section 2 we describe several DG methods for li...
متن کاملAdaptive FEM with Optimal Convergence Rates for a Certain Class of Nonsymmetric and Possibly Nonlinear Problems
We analyze adaptive mesh-refining algorithms for conforming finite element discretizations of certain non-linear second-order partial differential equations. We allow continuous polynomials of arbitrary, but fixed polynomial order. The adaptivity is driven by the residual error estimator. We prove convergence even with optimal algebraic convergence rates. In particular, our analysis covers gene...
متن کاملElasto-plastic analysis of discontinuous medium using linearly conforming radial point interpolation method
In this paper, the linearly conforming enriched radial basis point interpolation method is implemented for the elasto-plastic analysis of discontinuous medium. The linear conformability of the method is satisfied by the application of stabilized nodal integration and the enrichment of radial basis functions is achieved by the addition of linear polynomial terms. To implement the method for the ...
متن کاملSmoothed Aggregation Multigrid for the Discontinuous Galerkin Method
The aim of this paper is to investigate theoretically as well as experimentally an algebraic multilevel algorithm for the solution of the linear systems arising from the discontinuous Galerkin method. The smoothed aggregation multigrid, introduced by Vaněk for the conforming finite element method, is applied to low-order discretizations of convection-diffusion equations. For the elliptic model ...
متن کاملNew Method for Large Deflection Analysis of an Elliptic Plate Weakened by an Eccentric Circular Hole
The bending analysis of moderately thick elliptic plates weakened by an eccentric circular hole has been investigated in this article. The nonlinear governing equations have been presented by considering the von-Karman assumptions and the first-order shear deformation theory in cylindrical coordinates system. Semi-analytical polynomial method (SAPM) which had been presented by the author before...
متن کامل