
Fast largescale boundary element algorithms
Boundary element methods (BEM) reduce a partial differential equation in...
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A stabilizer free weak Galerkin finite element method on polytopal mesh: Part III
A weak Galerkin (WG) finite element method without stabilizers was intro...
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Convergence analysis of a CrankNicolson Galerkin method for an inverse source problem for parabolic systems with boundary observations
This work is devoted to an inverse problem of identifying a source term ...
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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 facto...
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Weak convergence rates for an explicit fulldiscretization of stochastic AllenCahn equation with additive noise
We discretize the stochastic AllenCahn equation with additive noise by ...
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Adaptive isogeometric boundary element methods with local smoothness control
In the frame of isogeometric analysis, we consider a Galerkin boundary e...
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A locally mass conserving quadratic velocity, linear pressure element
By supplementing the pressure space for the TaylorHood element a triang...
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Convergence analysis of oversampled collocation boundary element methods in 2D
Collocation boundary element methods for integral equations are easier to implement than Galerkin methods because the elements of the discretization matrix are given by lowerdimensional integrals. For that same reason, the matrix assembly also requires fewer computations. However, collocation methods typically yield slower convergence rates and less robustness, compared to Galerkin methods. We explore the extent to which oversampled collocation can improve both robustness and convergence rates. We show that in some cases convergence rates can actually be higher than the corresponding Galerkin method, although this requires oversampling at a faster than linear rate. In most cases of practical interest, oversampling at least lowers the error by a constant factor. This can still be a substantial improvement: we analyze an example where linear oversampling by a constant factor J (leading to a rectangular system of size JN × N) improves the error at a cubic rate in the constant J. Furthermore, the oversampled collocation method is much less affected by a poor choice of collocation points, as we show how oversampling can lead to guaranteed convergence. Numerical experiments are included for the twodimensional Helmholtz equation.
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