Adaptive data distribution for concurrent continuation.
Adaptive finite element methods for elliptic problems: Abstract framework and applications
We consider a general abstract framework of a continuous elliptic problem set on a Hilbert space V that is approximated by a family of (discrete) problems set on a finite-dimensional space of finite dimension not necessarily included into V. We give a series of realistic conditions on an error estimator that allows to conclude that the marking strategy of bulk type leads to the geometric convergence of the adaptive algorithm. These conditions are then verified for different concrete problems...
Adaptive mixed hybrid and macro-hybrid finite element methods.
Adaptive reduction-based multigrid for nearly singular and highly disordered physical systems.
Adaptivity and variational stabilization for convection-diffusion equations
In this paper we propose and analyze stable variational formulations for convection diffusion problems starting from concepts introduced by Sangalli. We derive efficient and reliable a posteriori error estimators that are based on these formulations. The analysis of resulting adaptive solution concepts, when specialized to the setting suggested by Sangalli’s work, reveals partly unexpected phenomena related to the specific nature of the norms induced by the variational formulation. Several remedies,...
Adaptivity and variational stabilization for convection-diffusion equations∗
In this paper we propose and analyze stable variational formulations for convection diffusion problems starting from concepts introduced by Sangalli. We derive efficient and reliable a posteriori error estimators that are based on these formulations. The analysis of resulting adaptive solution concepts, when specialized to the setting suggested by Sangalli’s work, reveals partly unexpected phenomena related to the specific nature of the norms induced by the variational formulation. Several remedies,...
Addendum to the paper “Finite element solution of quasistationary nonlinear magnetic field”
Addendum to the paper “Numerical solution of second-order equations on plane domains”
Additive Schwarz methods for the p-version finite element method.
Advances techniques for the direct, numerical solution of Poisson's equation
Advancing analysis capabilities in ANSYS through solver technology.
ALBERT---Software for scientific computations and applications.
Algebraic approach to domain decomposition
An iterative procedure containing two parameters for solving linear algebraic systems originating from the domain decomposition technique is proposed. The optimization of the parameters is investigated. A numerical example is given as an illustration.
Algebraic domain decomposition solver for linear elasticity
We generalize the overlapping Schwarz domain decomposition method to problems of linear elasticity. The convergence rate independent of the mesh size, coarse-space size, Korn’s constant and essential boundary conditions is proved here. Abstract convergence bounds developed here can be used for an analysis of the method applied to singular perturbations of other elliptic problems.
Algebraic Multi Level Preconditioning Methods. I.
Algebraic multigrid smoothing property of Kaczmarz's relaxation for general rectangular linear systems.
Algorithm 48. Solving boundary value problems for the biharmonic equation by the method of summary representations
Algorithmique et calculs de complexité pour un solveur de type dissections emboîtées.
All-at-once preconditioning in PDE-constrained optimization
The optimization of functions subject to partial differential equations (PDE) plays an important role in many areas of science and industry. In this paper we introduce the basic concepts of PDE-constrained optimization and show how the all-at-once approach will lead to linear systems in saddle point form. We will discuss implementation details and different boundary conditions. We then show how these system can be solved efficiently and discuss methods and preconditioners also in the case when bound...
Alternating direction Galerkin method with capacitance matrix for the parabolic problem with natural boundary condition