A splitting/polynomial chaos expansion approach for stochastic evolution equations
In this paper, we combine deterministic splitting methods with a polynomial chaos expansion method for solving stochastic parabolic evolution problems. The stochastic differential equation is reduced to a system of deterministic equations that we solve efficiently by splitting methods. The method ca...
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| Veröffentlicht in: | Journal of evolution equations 2021-06, Vol.21 (2), p.1345-1381 |
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| container_end_page | 1381 |
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| container_issue | 2 |
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| container_title | Journal of evolution equations |
| container_volume | 21 |
| creator | Kofler, Andreas Levajković, Tijana Mena, Hermann Ostermann, Alexander |
| description | In this paper, we combine deterministic splitting methods with a polynomial chaos expansion method for solving stochastic parabolic evolution problems. The stochastic differential equation is reduced to a system of deterministic equations that we solve efficiently by splitting methods. The method can be applied to a wide class of problems where the related stochastic processes are given uniquely in terms of stochastic polynomials. A comprehensive convergence analysis is provided and numerical experiments validate our approach. |
| doi_str_mv | 10.1007/s00028-020-00627-5 |
| format | Article |
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Evol. Equ</addtitle><description>In this paper, we combine deterministic splitting methods with a polynomial chaos expansion method for solving stochastic parabolic evolution problems. The stochastic differential equation is reduced to a system of deterministic equations that we solve efficiently by splitting methods. The method can be applied to a wide class of problems where the related stochastic processes are given uniquely in terms of stochastic polynomials. A comprehensive convergence analysis is provided and numerical experiments validate our approach.</description><subject>Analysis</subject><subject>Differential equations</subject><subject>Evolution</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Polynomials</subject><subject>Splitting</subject><subject>Stochastic processes</subject><issn>1424-3199</issn><issn>1424-3202</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9UMFKAzEUDKJgrf6ApwXPa1-yySY5lqJWKAii55BNk3bLdrNNdsX-vamrePP0hvdm5g2D0C2GewzAZxEAiMiBQA5QEp6zMzTBlNC8IEDOfzGW8hJdxbgDwJwJNkGv8yx2Td33dbuZdb45tn5f6yYzW-1jZj873cbat5nuuuC12WbOhyz2Pt1jX5vMfvhm6E8Mexj0CcRrdOF0E-3Nz5yi98eHt8UyX708PS_mq9ykHH1emlJSbV1FJbFyXWGHK7BACuAMDLW0oNQ4bk1aSyk0qxxx5VowKgTjJS2m6G70TckOg4292vkhtOmlIoyWwLlgOLHIyDLBxxisU12o9zocFQZ16k6N3anUnfruTrEkKkZRTOR2Y8Of9T-qL1rIcqQ</recordid><startdate>20210601</startdate><enddate>20210601</enddate><creator>Kofler, Andreas</creator><creator>Levajković, Tijana</creator><creator>Mena, Hermann</creator><creator>Ostermann, Alexander</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-1491-9056</orcidid></search><sort><creationdate>20210601</creationdate><title>A splitting/polynomial chaos expansion approach for stochastic evolution equations</title><author>Kofler, Andreas ; Levajković, Tijana ; Mena, Hermann ; Ostermann, Alexander</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-6c694aefb492e9db1f1b0e0230750c4e4344cf7ec1b0998a5bf2f6d8548857643</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Analysis</topic><topic>Differential equations</topic><topic>Evolution</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Polynomials</topic><topic>Splitting</topic><topic>Stochastic processes</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kofler, Andreas</creatorcontrib><creatorcontrib>Levajković, Tijana</creatorcontrib><creatorcontrib>Mena, Hermann</creatorcontrib><creatorcontrib>Ostermann, Alexander</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of evolution equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kofler, Andreas</au><au>Levajković, Tijana</au><au>Mena, Hermann</au><au>Ostermann, Alexander</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A splitting/polynomial chaos expansion approach for stochastic evolution equations</atitle><jtitle>Journal of evolution equations</jtitle><stitle>J. 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| language | eng |
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| subjects | Analysis Differential equations Evolution Mathematical analysis Mathematics Mathematics and Statistics Polynomials Splitting Stochastic processes |
| title | A splitting/polynomial chaos expansion approach for stochastic evolution equations |
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