Error estimation and adaptivity for stochastic collocation finite elements part I: single-level approximation
A general adaptive refinement strategy for solving linear elliptic partial differential equations
with random data is proposed and analysed herein. The adaptive strategy extends the a …
with random data is proposed and analysed herein. The adaptive strategy extends the a …
Error estimation and adaptivity for stochastic collocation finite elements Part II: multilevel approximation
A multilevel adaptive refinement strategy for solving linear elliptic partial differential
equations with random data is recalled in this work. The strategy extends the a posteriori …
equations with random data is recalled in this work. The strategy extends the a posteriori …
Convergence and rate optimality of adaptive multilevel stochastic Galerkin FEM
We analyze an adaptive algorithm for the numerical solution of parametric elliptic partial
differential equations in two-dimensional physical domains, with coefficients and right-hand …
differential equations in two-dimensional physical domains, with coefficients and right-hand …
Rational-based model order reduction of Helmholtz frequency response problems with adaptive finite element snapshots
We introduce several spatially adaptive model order reduction approaches tailored to non-
coercive elliptic boundary value problems, specifically, parametric-in-frequency Helmholtz …
coercive elliptic boundary value problems, specifically, parametric-in-frequency Helmholtz …
Adaptive nonintrusive reconstruction of solutions to high-dimensional parametric PDEs
Numerical methods for random parametric PDEs can greatly benefit from adaptive
refinement schemes, in particular when functional approximations are computed as in …
refinement schemes, in particular when functional approximations are computed as in …
[BOOK][B] Adaptive and non-intrusive uncertainty quantification for high-dimensional parametric PDEs
N Farchmin - 2022 - search.proquest.com
Diese Dissertation beschäftigt sich mit der Kombination aus verlässlicher Fehlerkontrolle
und datenbasierter Approximation um nicht-intrusive und zuverlässige Algorithmen zur …
und datenbasierter Approximation um nicht-intrusive und zuverlässige Algorithmen zur …
Rational-approximation-based model order reduction of Helmholtz frequency response problems with adaptive finite element snapshots
We introduce several spatially adaptive model order reduction approaches tailored to non-
coercive elliptic boundary value problems, specifically, parametric-in-frequency Helmholtz …
coercive elliptic boundary value problems, specifically, parametric-in-frequency Helmholtz …
Guaranteed quasi-error reduction of adaptive Galerkin FEM for parametric PDEs with lognormal coefficients
M Eigel, N Hegemann - arxiv preprint arxiv:2302.02839, 2023 - arxiv.org
Solving high-dimensional random parametric PDEs poses a challenging computational
problem. It is well-known that numerical methods can greatly benefit from adaptive …
problem. It is well-known that numerical methods can greatly benefit from adaptive …
Goal-oriented adaptive multilevel stochastic Galerkin FEM
This paper is concerned with the numerical approximation of quantities of interest
associated with solutions to parametric elliptic partial differential equations (PDEs). We …
associated with solutions to parametric elliptic partial differential equations (PDEs). We …
Two-level error estimation for the integral fractional Laplacian
M Faustmann, EP Stephan… - Computational Methods in …, 2023 - degruyter.com
For the singular integral definition of the fractional Laplacian, we consider an adaptive finite
element method steered by two-level error indicators. For this algorithm, we show linear …
element method steered by two-level error indicators. For this algorithm, we show linear …