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Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs *

Schwab, Christoph ; Gittelson, Claude Jeffrey

Acta Numerica, 2011, Vol.20, pp.291-467 [Peer Reviewed Journal]

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Fast evaluation of nonlinear functionals of tensor product wavelet expansions

Schwab, Christoph ; Stevenson, Rob

Numerische Mathematik, 2011, Vol.119(4), pp.765-786 [Peer Reviewed Journal]

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Exponential Convergence of Gauss--Jacobi Quadratures for Singular Integrals over Simplices in Arbitrary Dimension

Chernov, Alexey ; Schwab, Christoph

SIAM Journal on Numerical Analysis, 2012, pp.1433-1455 [Peer Reviewed Journal]

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4
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High-order finite element approximation for partial differential equations

Chernov, Alexey ; Schwab, Christoph

Computers and Mathematics with Applications, March 2014, Vol.67(4), pp.709-711 [Peer Reviewed Journal]

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5
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TENSOR-STRUCTURED GALERKIN APPROXIMATION OF PARAMETRIC AND STOCHASTIC ELLIPTIC PDEs*

Khoromskij, Boris ; Schwab, Christoph

SIAM Journal on Scientific Computing, 2011, pp.364-385 [Peer Reviewed Journal]

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6
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Scaling limits in computational Bayesian inversion

Schillings, Claudia ; Schwab, Christoph

ESAIM. Mathematical Modelling and Numerical Analysis, Nov-Dec 2016 [Peer Reviewed Journal]

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7
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Sparse Tensor Galerkin Discretization of Parametric and Random Parabolic PDEs---Analytic Regularity and Generalized Polynomial Chaos Approximation

Hoang, Viet ; Schwab, Christoph

SIAM Journal on Mathematical Analysis, 2013, Vol.45(5), pp.3050-3083 [Peer Reviewed Journal]

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8
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Sparse, adaptive smolyak quadratures for bayesian inverse problems

Schillings, Claudia ; Schwab, Christoph

Inverse Problems, 2013, Vol.29(6), p.065011 (28pp) [Peer Reviewed Journal]

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9
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High order approximation of probabilistic shock profiles in hyperbolic conservation laws with uncertain initial data

Schwab, Christoph ; Tokareva, Svetlana

ESAIM. Mathematical Modelling and Numerical Analysis, May 2013, pp.807-835 [Peer Reviewed Journal]

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10
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Sparse tensor finite elements for elliptic multiple scale problems

Harbrecht, Helmut ; Schwab, Christoph

Computer Methods in Applied Mechanics and Engineering, 2011, Vol.200(45), pp.3100-3110 [Peer Reviewed Journal]

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11
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Sparse Adaptive Approximation of High Dimensional Parametric Initial Value Problems

Hansen, Markus ; Schwab, Christoph

Vietnam Journal of Mathematics, 2013, Vol.41(2), pp.181-215 [Peer Reviewed Journal]

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12
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Quantized tensor-structured finite elements for second-order elliptic PDEs in two dimensions

Kazeev, Vladimir ; Schwab, Christoph

Numerische Mathematik, 2018, Vol.138(1), pp.133-190 [Peer Reviewed Journal]

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13
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Sparse-grid, reduced-basis Bayesian inversion

Chen, Peng ; Schwab, Christoph

Computer Methods in Applied Mechanics and Engineering, 01 December 2015, Vol.297, pp.84-115 [Peer Reviewed Journal]

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14
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Analytic Regularity and GPC Approximation for Control Problems Constrained by Linear Parametric Elliptic and Parabolic PDEs

Kunoth, Angela ; Schwab, Christoph

SIAM Journal on Control and Optimization, 2013, Vol.51(3), pp.2442-2471 [Peer Reviewed Journal]

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15
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Space–time hp -approximation of parabolic equations

Devaud, Denis ; Schwab, Christoph

Calcolo, 2018, Vol.55(3), pp.1-23 [Peer Reviewed Journal]

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16
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Sparse-grid, reduced-basis Bayesian inversion: Nonaffine-parametric nonlinear equations

Chen, Peng ; Schwab, Christoph

Journal of Computational Physics, 01 July 2016, Vol.316, pp.470-503 [Peer Reviewed Journal]

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17
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Optimality of adaptive Galerkin methods for random parabolic partial differential equations

Jeffrey Gittelson, Claude ; Andreev, Roman ; Schwab, Christoph

Journal of computational and applied mathematics, 2014, Vol.263(1), pp.189-201 [Peer Reviewed Journal]

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18
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Efficient Characterization of Parametric Uncertainty of Complex (Bio)chemical Networks (Efficient Characterization of Parametric Uncertainty)

Schillings, Claudia ; Sunnåker, Mikael ; Stelling, Jörg ; Schwab, Christoph ;Maranas, Costas D. (Editor)

2015, Vol.11(8), p.e1004457 [Peer Reviewed Journal]

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19
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Electromagnetic wave scattering by random surfaces: uncertainty quantification via sparse tensor boundary elements

Jerez - Hanckes, Carlos ; Schwab, Christoph

IMA Journal of Numerical Analysis, 2017, Vol. 37(3), pp.1175-1210 [Peer Reviewed Journal]

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Exponential Convergence of hp -FEM for Elliptic Problems in Polyhedra: Mixed Boundary Conditions and Anisotropic Polynomial Degrees

Schötzau, Dominik ; Schwab, Christoph

Foundations of Computational Mathematics, 2018, Vol.18(3), pp.595-660 [Peer Reviewed Journal]

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