Journal
SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume 57, Issue 5, Pages 2359-2382Publisher
SIAM PUBLICATIONS
DOI: 10.1137/18M1229560
Keywords
adaptive methods; a posteriori error analysis; two-level error estimate; stochastic Galerkin methods; finite element methods; parametric PDEs
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Funding
- EPSRC [EP/P013791/1]
- Alan Turing Institute under the EPSRC [EP/N510129/1]
- Austrian Science Fund (FWF) [W1245, F65]
- EPSRC [EP/P013791/1] Funding Source: UKRI
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We propose and analyze novel adaptive algorithms for the numerical solution of elliptic partial differential equations with parametric uncertainty. Four different marking strategies are employed for refinement of stochastic Galerkin finite element approximations. The algorithms are driven by the energy error reduction estimates derived from two-level a posteriori error indicators for spatial approximations and hierarchical a posteriori error indicators for parametric approximations. The focus of this work is on the mathematical foundation of the adaptive algorithms in the sense of rigorous convergence analysis. In particular, we prove that the proposed algorithms drive the underlying energy error estimates to zero.
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