Acceleration of convergence of a two-level algorithm by smoothing transfer operators
The technique for accelerating the convergence of the algebraic multigrid method is proposed.
Acceleration of two-grid stabilized mixed finite element method for the Stokes eigenvalue problem
This paper provides an accelerated two-grid stabilized mixed finite element scheme for the Stokes eigenvalue problem based on the pressure projection. With the scheme, the solution of the Stokes eigenvalue problem on a fine grid is reduced to the solution of the Stokes eigenvalue problem on a much coarser grid and the solution of a linear algebraic system on the fine grid. By solving a slightly different linear problem on the fine grid, the new algorithm significantly improves the theoretical error...
Accurate and online-efficient evaluation of the a posteriori error bound in the reduced basis method
The reduced basis method is a model reduction technique yielding substantial savings of computational time when a solution to a parametrized equation has to be computed for many values of the parameter. Certification of the approximation is possible by means of an a posteriori error bound. Under appropriate assumptions, this error bound is computed with an algorithm of complexity independent of the size of the full problem. In practice, the evaluation of the error bound can become very sensitive...
Adaptive algorithm for stochastic Galerkin method
We introduce a new tool for obtaining efficient a posteriori estimates of errors of approximate solutions of differential equations the data of which depend linearly on random parameters. The solution method is the stochastic Galerkin method. Polynomial chaos expansion of the solution is considered and the approximation spaces are tensor products of univariate polynomials in random variables and of finite element basis functions. We derive a uniform upper bound to the strengthened Cauchy-Bunyakowski-Schwarz...
Adaptive Boundary Element Methods for Strongly Elliptic Integral Equations.
Adaptive coupling of boundary elements and finite elements
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.