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A Neumann-Neumann algorithm for a mortar discretization of elliptic problems with discontinuous coefficients
Neumann-Neumann algorithm have been well developed for standard finite element discretization of elliptic problems with discontinuous coefficients....
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Sensitivity and Approximation of Coupled Fluid-Structure Equations by Virtual Control Method
The formulation of a particular fluid--structure interaction as an optimal control problem is the departure point of this work. The control is the...
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Hierarchical Riesz Bases for Hs(Ω), 1 < s < 5/2
On arbitrary polygonal domains $\Omega \subset \RR^2$, we construct $C^1$ hierarchical Riesz bases for Sobolev spaces $H^s(\Omega)$. In contrast to...
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A convergence theory for an overlap** Schwarz algorithm using discontinuous iterates
A new type of overlap** Schwarz methods, using discontinuous iterates, is constructed by modifying the classical overlap** Schwarz algorithm....
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Stop** criteria for iterations in finite element methods
This work extends the results of Arioli [1], [2] on stop** criteria for iterative solution methods for linear finite element problems to the case...
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A New Kind of Trivariate C 1 Macro-element
We propose a construction of a trivariate C 1 macro-element over a special tetrahedral partition and compare our construction with known C 1 ...
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Aubin—Nitsche Estimates Are Equivalent to Compact Embeddings
In this short note we show that having an Aubin–Nitsche type estimate (a superconvergence estimate in a weaker norm for a convergent Galerkin method)...
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Linear-programming approach to nonconvex variational problems
In nonconvex optimization problems, in particular in nonconvex variational problems, there usually does not exist any classical solution but only...
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Finite Element Analysis of Free Material Optimization Problem
Free material optimization solves an important problem of structural engineering, i.e. to find the stiffest structure for given loads and boundary...
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Discontinuous Stable Elements for the Incompressible Flow
In this paper, we derive a discontinuous Galerkin finite element formulation for the Stokes equations and a group of stable elements associated with...
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Uniformly Convergent Multigrid Methods for Convection–Diffusion Problems without Any Constraint on Coarse Grids
We construct a class of multigrid methods for convection–diffusion problems. The proposed algorithms use first order stable monotone schemes to...
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Paley—Wiener Theorems and Shannon Sampling in the Clifford Analysis Setting
This paper is concerned with the classical Paley—Wiener theorems in one and several complex variables, the generalization to Euclidean spaces in the...
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Error estimates for mixed finite element approximations to a linear Stefan problem
We introduce a semidiscrete mixed finite element approximation for the single-phase linear Stefan problem and show the unique existence of the...
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Preconditioners for the pressure-correction method applied to the unsteady stokes problem
In this paper, the unsteady Stokes problem is considered and also the pressure-correction method for the problem is described. At a fixed time level,...
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A discrete finite element galerkin method for a unidimensional single-phase Stefan problem
Based on Landau-type transformation, a Stefan problem with nonlinear free boundary condition is transformed into a system consisting of parabolic...
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A characteristics-mixed finite element method for Burgers’ equation
In this paper, we propose a new mixed finite element method, called the characteristics-mixed method, for approximating the solution to Burgers’...
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Rigorous Numerics for Dissipative Partial Differential Equations II. Periodic Orbit for the Kuramoto–Sivashinsky PDE—A Computer-Assisted Proof
We present a method of self-consistent a priori bounds, which allows us to study rigorously the dynamics of dissipative PDEs. As an application we...
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Preconditioning Techniques for Newton's Method for the Incompressible Navier–Stokes Equations
Newton's method for the incompressible Navier—Stokes equations gives rise to large sparse non-symmetric indefinite matrices with a so-called...
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A Survey of Algebraic Multilevel Iteration (AMLI) Methods
For the solution by preconditioned conjugate gradient methods of symmetric positive definite equations as arising in boundary value problems we...
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An Adaptive Mesh-Refining Algorithm Allowing for an H 1 Stable L 2 Projection onto Courant Finite Element Spaces
Suppose $\cal{S}^1({\cal T})\subset H^1(\Omega)$ is the $P_1$-finite element space of $\cal{T}$-piecewise affine functions based on a regular...