
Discontinuous Galerkin Finite Element Methods for 1D Rosenau Equation
In this paper, discontinuous Galerkin finite element methods are applied...
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Truncation Preconditioners for Stochastic Galerkin Finite Element Discretizations
Stochastic Galerkin finite element method (SGFEM) provides an efficient ...
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Discontinuous Galerkin and C^0IP finite element approximation of periodic Hamilton–Jacobi–Bellman–Isaacs problems with application to numerical homogenization
In the first part of the paper, we study the discontinuous Galerkin (DG)...
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Domain decomposition preconditioners for highorder discretisations of the heterogeneous Helmholtz equation
We consider onelevel additive Schwarz domain decomposition precondition...
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Stochastic Discontinuous Galerkin Methods for Robust Deterministic Control of Convection Diffusion Equations with Uncertain Coefficients
We investigate a numerical behaviour of robust deterministic optimal con...
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Wavenumberexplicit convergence of the hpFEM for the fullspace heterogeneous Helmholtz equation with smooth coefficients
A convergence theory for the hpFEM applied to a variety of constantcoe...
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Parameterrobust Stochastic Galerkin mixed approximation for linear poroelasticity with uncertain inputs
Linear poroelasticity models have a number of important applications in ...
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Analysis of a Helmholtz preconditioning problem motivated by uncertainty quantification
This paper analyses the following question: let A_j, j=1,2, be the Galerkin matrices corresponding to finiteelement discretisations of the exterior Dirichlet problem for the heterogeneous Helmholtz equations ∇· (A_j ∇ u_j) + k^2 n_j u_j= f. How small must A_1 A_2_L^q and n_1  n_2_L^q be (in terms of kdependence) for GMRES applied to either (A_1)^1A_2 or A_2(A_1)^1 to converge in a kindependent number of iterations for arbitrarily large k? (In other words, for A_1 to be a good left or rightpreconditioner for A_2?). We prove results answering this question, give theoretical evidence for their sharpness, and give numerical experiments supporting the estimates. Our motivation for tackling this question comes from calculating quantities of interest for the Helmholtz equation with random coefficients A and n. Such a calculation may require the solution of many deterministic Helmholtz problems, each with different A and n, and the answer to the question above dictates to what extent a previouslycalculated inverse of one of the Galerkin matrices can be used as a preconditioner for other Galerkin matrices.
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