Wavelet boundary element methods – Adaptivity and goal-oriented error estimation

This article is dedicated to the adaptive wavelet boundary element method. It computes an approximation to the unknown solution of the boundary integral equation under consideration with a rate $N^{−s}_{dof}$, whenever the solution can be approximated with this rate in the setting determined by the underlying wavelet basis. The computational cost scale linearly in the number $N_{dof}$ of degrees of freedom. Goal-oriented error estimation for evaluating linear output functionals of the solution is also considered. An algorithm is proposed that approximately evaluates a linear output functional with a rate $N^{−(s+t)}_{dof}$, whenever the primal solution can be approximated with a rate $N^{-s}_{dof}$ and the dual solution can be approximated with a rate $N^{−t}_{dof}$, while the cost still scale linearly in $N_{dof}$. Numerical results for an acoustic scattering problem and for the point evaluation of the potential in case of the Laplace equation are reported to validate and quantify the approach

Inverse inequalities on non-quasi-uniform meshes and application to the mortar element method

We present a range of mesh-dependent inequalities for piecewise constant and continuous piecewise linear finite element functions u defined on locally refined shape-regular (but possibly non-quasi-uniform) meshes. These inequalities involve norms of the form ∥h α u∥ W s,p (Ω) for positive and negative s and α, where h is a function which reflects the local mesh diameter in an appropriate way. The only global parameter involved is N, the total number of degrees of freedom in the finite element space, and we avoid estimates involving either the global maximum or minimum mesh diameter. Our inequalities include new variants of inverse inequalities as well as trace and extension theorems. They can be used in several areas of finite element analysis to extend results – previously known only for quasi-uniform meshes – to the locally refined case. Here we describe applications to (i) the theory of nonlinear approximation and (ii) the stability of the mortar element method for locally refined meshes

Inverse Inequalities on Non-Quasiuniform Meshes and Application to the Mortar Element Method

We present a range of mesh-dependent inequalities for piecewise constant and continuous piecewise linear finite element functions u defined on locally refined shape-regular (but possibly non-quasiuniform) meshes. These inequalities involve norms of the form kh ff uk W s;p(\Omega\Gamma for positive and negative s and ff, where h is a function which reflects the local mesh diameter in an appropriate way. The only global parameter involved is N , the total number of degrees of freedom in the finite element space, and we avoid estimates involving either the global maximum or minimum mesh diameter. Our inequalities include new variants of inverse inequalities as well as trace and extension theorems. They can be used in several areas of finite element analysis to extend results - previously known only for quasiuniform meshes - to the locally refined case. Here we describe applications to: (i) the theory of nonlinear approximation and (ii) the stability of the mortar element method for locally refined meshes

Inverse inequalities for non-quasiuniform meshes and applications to the mortar element method

Abstract. We present a range of mesh-dependent inequalities for piecewise constant and continuous piecewise linear finite element functions u defined on locally refined shape-regular (but possibly non-quasi-uniform) meshes. These inequalities involve norms of the form �h α u � W s,p (Ω) for positive and negative s and α, where h is a function which reflects the local mesh diameter in an appropriate way. The only global parameter involved is N, the total number of degrees of freedom in the finite element space, and we avoid estimates involving either the global maximum or minimum mesh diameter. Our inequalities include new variants of inverse inequalities as well as trace and extension theorems. They can be used in several areas of finite element analysis to extend results—previously known only for quasi-uniform meshes—to the locally refined case. Here we describe applications to (i) the theory of nonlinear approximation and (ii) the stability of the mortar element method for locally refined meshes. 1

Vacinação da rubéola : risco teratogênico

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Vacinação da rubéola : risco teratogênico

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Vacinação da rubéola na gestação : risco teratogênico?

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Vacinação da rubéola na gestação : risco teratogênico?

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