A unified approach to a posteriori error estimation using element residual methods.
A unified convergence analysis for local projection stabilisations applied to the Oseen problem
The discretisation of the Oseen problem by finite element methods may suffer in general from two shortcomings. First, the discrete inf-sup (Babuška-Brezzi) condition can be violated. Second, spurious oscillations occur due to the dominating convection. One way to overcome both difficulties is the use of local projection techniques. Studying the local projection method in an abstract setting, we show that the fulfilment of a local inf-sup condition between approximation and projection spaces...
A uniformly accurate finite volume discretization for a convection-diffusion problem.
A variational method for electromagnetic diffraction in biperiodic structures
A variational method for parameter identification
A viscosity solution method for Shape-From-Shading without image boundary data
In this paper we propose a solution of the Lambertian shape-from-shading (SFS) problem by designing a new mathematical framework based on the notion of viscosity solution. The power of our approach is twofolds: (1) it defines a notion of weak solutions (in the viscosity sense) which does not necessarily require boundary data. Moreover, it allows to characterize the viscosity solutions by their “minimums”; and (2) it unifies the works of [Rouy and Tourin, SIAM J. Numer. Anal.29 (1992) 867–884],...
A wavelet multigrid preconditioner for Dirichlet boundary value problems in general domains
A weakly over-penalized symmetric interior penalty method.
A weakly over-penalized symmetric interior penalty method for the biharmonic problem.
A well-conditioned integral equation for iterative solution of scattering problems with a variable Leontovitch boundary condition
The construction of a well-conditioned integral equation for iterative solution of scattering problems with a variable Leontovitch boundary condition is proposed. A suitable parametrix is obtained by using a new unknown and an approximation of the transparency condition. We prove the well-posedness of the equation for any wavenumber. Finally, some numerical comparisons with well-tried method prove the efficiency of the new formulation.
About biharmonic problem via a spectral approach and decomposition techniques.
About Delaunay triangulations and discrete maximum principles for the linear conforming FEM applied to the Poisson equation
The starting point of the analysis in this paper is the following situation: “In a bounded domain in , let a finite set of points be given. A triangulation of that domain has to be found, whose vertices are the given points and which is ‘suitable’ for the linear conforming Finite Element Method (FEM).” The result of this paper is that for the discrete Poisson equation and under some weak additional assumptions, only the use of Delaunay triangulations preserves the maximum principle.
Abschnittzerlegungen bei oberen Schranken für Eigenwerte von Operatorpolynomen.
Acceleration of Convergence for Finite Element Solutions of the Poisson Equation.
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