
A mixed finite element method with piecewise linear elements for the biharmonic equation on surfaces
The biharmonic equation with Dirichlet and Neumann boundary conditions d...
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Quasioptimal adaptive mixed finite element methods for controlling natural norm errors
For a generalized HodgeLaplace equation, we prove the quasioptimal co...
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A probust polygonal discontinuous Galerkin method with minus one stabilization
We introduce a new stabilization for discontinuous Galerkin methods for ...
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Convergence analysis of oversampled collocation boundary element methods in 2D
Collocation boundary element methods for integral equations are easier t...
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Homogenization of the LandauLifshitz equation
In this paper, we consider homogenization of the LandauLifshitz equatio...
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Local energy estimates for the fractional Laplacian
The integral fractional Laplacian of order s ∈ (0,1) is a nonlocal opera...
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High order numerical schemes for transport equations on bounded domains
This article is an account of the NABUCO project achieved during the sum...
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L^∞ norm error estimates for HDG methods applied to the Poisson equation with an application to the Dirichlet boundary control problem
We prove quasioptimal L^∞ norm error estimates (up to logarithmic factors) for the solution of Poisson's problem by the standard Hybridizable Discontinuous Galerkin (HDG) method. Although such estimates are available for conforming and mixed finite element methods, this is the first proof for HDG. The method of proof is motivated by known L^∞ norm estimates for mixed finite elements. We show two applications: the first is to prove optimal convergence rates for boundary flux estimates, and the second is to prove that numerically observed convergence rates for the solution of a Dirichlet boundary control problem are to be expected theoretically. Numerical examples show that the predicted rates are seen in practice.
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