Domain decomposition and multigrid algorithms for elliptic problems on unstructured meshes.
Domain decomposition method and elastic multi-structures: the stiffened plate problem.
Domain decomposition methods and scientific computing applications
This paper reviews the basic mathematical ideas and convergence analysis of domain decomposition methods. These are parallel and scalable iterative methods for the efficient numerical solution of partial differential equations. Two examples are then presented showing the application of domain decomposition methods to large-scale numerical simulations in computational mechanics and electrocardiology.
Domain decomposition methods coupled with parareal for the transient heat equation in 1 and 2 spatial dimensions
We present a parallel solution algorithm for the transient heat equation in one and two spatial dimensions. The problem is discretized in space by the lowest-order conforming finite element method. Further, a one-step time integration scheme is used for the numerical solution of the arising system of ordinary differential equations. For the latter, the parareal method decomposing the time interval into subintervals is employed. It leads to parallel solution of smaller time-dependent problems. At...
Domain Embedding Methods for the Stokes Equations.
Domain optimization in -axisymmetric elliptic problems by dual finite element method
An axisymmetric second order elliptic problem with mixed boundary conditions is considered. The shape of the domain has to be found so as to minimize a cost functional, which is given in terms of the cogradient of the solution. A new dual finite element method is used for approximate solutions. The existence of an optimal domain is proven and a convergence analysis presented.
Domain optimization in axisymmetric elliptic boundary value problems by finite elements
An axisymmetric second order elliptic problem with mixed boundary conditions is considered. A part of the boundary has to be found so as to minimize one of four types of cost functionals. The existence of an optimal boundary is proven and a convergence analysis for piecewise linear approximate solutions presented, using weighted Sobolev spaces.
Dorr, M.R.: Error Estimates for the Combined h and p Versions of the Finite Element Method.
Dos algoritmos para la resolución numérica de una ecuación parabólica casi-lineal.
Double greedy algorithms: Reduced basis methods for transport dominated problems
The central objective of this paper is to develop reduced basis methods for parameter dependent transport dominated problems that are rigorously proven to exhibit rate-optimal performance when compared with the Kolmogorov n-widths of the solution sets. The central ingredient is the construction of computationally feasible “tight” surrogates which in turn are based on deriving a suitable well-conditioned variational formulation for the parameter dependent problem. The theoretical results are illustrated...
Dual combined finite element methods for non-newtonian flow (II). Parameter-dependent problem
Dual Combined Finite Element Methods For Non-Newtonian Flow (II) Parameter-Dependent Problem
This is the second part of the paper for a Non-Newtonian flow. Dual combined Finite Element Methods are used to investigate the little parameter-dependent problem arising in a nonliner three field version of the Stokes system for incompressible fluids, where the viscosity obeys a general law including the Carreau's law and the Power law. Certain parameter-independent error bounds are obtained which solved the problem proposed by Baranger in [4] in a unifying way. We also give some stable finite...
Dual finite element analysis for an inequality of the 2nd order
The dual variational formulation of some free boundary value problem is given and its approximation by finite element method is studied, using piecewise linear elements with non-positive divergence.
Dual finite element analysis for contact problem of elastic bodies with an enlarging contact zone
Dual finite element analysis of the contact problem of two elastic bodies with an enlarging contact zone is presented. Approximations of the solution are defined on two types of triangulations by piecewise constant stress fields. Convergence is proved in both cases.
Dual finite element analysis for elliptic problems with obstacles on the boundary. I
For an elliptic model problem with non-homogeneous unilateral boundary conditions, two dual variational formulations are presented and justified on the basis of a saddle point theorem. Using piecewise linear finite element models on the triangulation of the given domain, dual numerical procedures are proposed. By means of one-sided approximations, some a priori error estimates are proved, assuming that the solution is sufficiently smooth. A posteriori error estimates and two-sided bounds for the...
Dual finite element analysis for semi-coercive unilateral boundary value problems
Dual finite element analysis for unilateral boundary value problems
Dual finite element analysis of axisymmetric elliptic problems with an absolute term
A model second order elliptic equation in cylindrical coordinates with mixed boundary conditions is considered. A dual variational formulation is employed to calculate the cogradient of the solution directly. Approximations are defined on the basis of standard finite elements spaces. Convergence analysis and some a posteriori error estimates are presented.
Dual variational principles for an elliptic partial differential equation
Duality Estimates for the Numerical Solution of Integral Equations.