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
An a posteriori error analysis of adaptive finite element methods for distributed elliptic control problems with control constraints
We present an a posteriori error analysis of adaptive finite element approximations of distributed control problems for second order elliptic boundary value problems under bound constraints on the control. The error analysis is based on a residual-type a posteriori error estimator that consists of edge and element residuals. Since we do not assume any regularity of the data of the problem, the error analysis further invokes data oscillations. We prove reliability and efficiency of the error estimator...
An a posteriori error analysis of adaptive finite element methods for distributed elliptic control problems with control constraints
We present an a posteriori error analysis of adaptive finite element approximations of distributed control problems for second order elliptic boundary value problems under bound constraints on the control. The error analysis is based on a residual-type a posteriori error estimator that consists of edge and element residuals. Since we do not assume any regularity of the data of the problem, the error analysis further invokes data oscillations. We prove reliability and efficiency of the error estimator...
An a posteriori error estimate for the Stokes-Brinkman problem in a polygonal domain
We derive a residual based a posteriori error estimate for the Stokes-Brinkman problem on a two-dimensional polygonal domain. We use Taylor-Hood triangular elements. The link to the possible information on the regularity of the problem is discussed.
An a posteriori Error Estimation of the Rayleigh-Ritz Eigenvalues.
An Abbreviated Numerical Scheme for Linear Symmetric Hyperbolic Equations, n ... 2.
An accurate solution of the Poisson equation by the Legendre tau method.
An adaptive finite element method for solving a double well problem describing crystalline microstructure
The minimization of nonconvex functionals naturally arises in materials sciences where deformation gradients in certain alloys exhibit microstructures. For example, minimizing sequences of the nonconvex Ericksen-James energy can be associated with deformations in martensitic materials that are observed in experiments[2,3]. — From the numerical point of view, classical conforming and nonconforming finite element discretizations have been observed to give minimizers with their quality being highly dependent...
An adaptive finite element method in reconstruction of coefficients in Maxwell's equations from limited observations
We propose an adaptive finite element method for the solution of a coefficient inverse problem of simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions in the Maxwell's system using limited boundary observations of the electric field in 3D. We derive a posteriori error estimates in the Tikhonov functional to be minimized and in the regularized solution of this functional, as well as formulate the corresponding adaptive algorithm. Our numerical experiments...
An Adaptive Newton Algorithm Based on Numerical Inversion: Regularization as Postconditioner.
An adaptive numerical method for the wave equation with a nonlinear boundary condition.
An Adaptive Quadrilateral Mesh in Curved Domains
An nonlinear elliptic system for generating adaptive quadrilateral meshes in curved domains is presented. The presented technique has been implemented in the C++ language with the help of the standard template library. The software package writes the converged meshes in the GMV and the Matlab formats. Grid generation is the first very important step for numerically solving partial differential equations. Thus, the presented C++ grid generator is extremely important to the computational science community....
An additive Schwarz method for mortar Morley finite element discretizations of 4th order elliptic problem in 2D.
An aggregation-based algebraic multigrid method.
An alternating direction implicit method for orthogonal spline collocation linear systems.
An alternating-direction iteration method for Helmholtz problems
An alternating-direction iterative procedure is described for a class of Helmholz-like problems. An algorithm for the selection of the iteration parameters is derived; the parameters are complex with some having positive real part and some negative, reflecting the noncoercivity and nonsymmetry of the finite element or finite difference matrix. Examples are presented, with an applications to wave propagation.