Adaptive stochastic Galerkin finite element methods: Optimality and non-affine coefficients
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910890288218112 |
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| author | Bachmayr, Markus Eisenmann, Henrik Voulis, Igor |
| author_facet | Bachmayr, Markus Eisenmann, Henrik Voulis, Igor |
| contents | Near-optimal computational complexity of an adaptive stochastic Galerkin method with independently refined spatial meshes for elliptic partial differential equations is shown. The method takes advantage of multilevel structure in expansions of random diffusion coefficients and combines operator compression in the stochastic variables with error estimation using finite element frames in space. A new operator compression strategy is introduced for nonlinear coefficient expansions, such as diffusion coefficients with log-affine structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18704 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Adaptive stochastic Galerkin finite element methods: Optimality and non-affine coefficients Bachmayr, Markus Eisenmann, Henrik Voulis, Igor Numerical Analysis 35J25, 35R60, 41A10, 41A63, 42C10, 65N50, 65N30 Near-optimal computational complexity of an adaptive stochastic Galerkin method with independently refined spatial meshes for elliptic partial differential equations is shown. The method takes advantage of multilevel structure in expansions of random diffusion coefficients and combines operator compression in the stochastic variables with error estimation using finite element frames in space. A new operator compression strategy is introduced for nonlinear coefficient expansions, such as diffusion coefficients with log-affine structure. |
| title | Adaptive stochastic Galerkin finite element methods: Optimality and non-affine coefficients |
| topic | Numerical Analysis 35J25, 35R60, 41A10, 41A63, 42C10, 65N50, 65N30 |
| url | https://arxiv.org/abs/2503.18704 |