Research

Numerics of PDEs
Finite Element Methods
contractive iterative solvers
optimal computational cost of adaptive FEM

P. Bringmann, M. Feischl, A. Miraçi, D. Praetorius, J. Streitberger: On full linear convergence and optimal complexity of adaptive FEM with inexact solver, Computers & Mathematics with Applications, accepted for publication (2024). [arXiv:2311.15738]
P. Bringmann, M. Brunner, D. Praetorius, J. Streitberger: Optimal complexity of goal-oriented adaptive FEM for nonsymmetric linear elliptic PDEs, Journal of Numerical Mathematics, online veröffentlicht (2024). [www] (open access). [arXiv:2312.00489]
M. Brunner, D. Praetorius, J. Streitberger: Cost-optimal adaptive FEM for semilinear elliptic PDEs, akzeptiert zur Veröffentlichung in Proceedings of ENUMATH 2023 (2024).
M. Brunner, D. Praetorius, J. Streitberger: Optimal cost of (goal-oriented) adaptive FEM for general second-order linear elliptic PDEs, akzeptiert zur Veröffentlichung in Proceedings of ENUMATH 2023 (2024).
M. Innerberger, A. Miraçi, D. Praetorius, J. Streitberger: hp-robust multigrid solver on locally refined meshes for FEM discretizations of symmetric elliptic PDEs, ESAIM: Mathematical Modelling and Numerical Analysis, 58 (2024), 247–272. [www] (open access), [arXiv:2210.10415]
P. Bringmann, C. Carstensen, J. Streitberger: Local parameter selection in the C⁰ interior penalty method for the biharmonic equation, Journal of Numerical Mathematics, 32 (2024), 257-273. [www] (open access), [arXiv:2209.05221]
M. Brunner, P. Heid, M. Innerberger, A. Miraçi, D. Praetorius, J. Streitberger: Adaptive FEM with quasi-optimal overall cost for nonsymmetric linear elliptic PDEs, IMA Journal of Numerical Analysis, 44 (2024), 1560–1596 and 1903–1909. [www] (open access), [corrigendum] (open access), [arXiv:2212.00353]

A. Miraçi, D. Praetorius, J. Streitberger: Parameter-robust full linear convergence and optimal complexity of adaptive iteratively linearized FEM for nonlinear PDEs, [arXiv:2401.17778], 2024
M. Brunner, D. Praetorius, J. Streitberger: Cost-optimal adaptive FEM with linearization and algebraic solver for semilinear elliptic PDEs, [arXiv:2401.06486], 2024
P. Bringmann, M. Feischl, A. Miraçi, D. Praetorius, J. Streitberger: On full linear convergence and optimal complexity of adaptive FEM with inexact solver, [arXiv:2311.15738], 2023

P. Bringmann, M. Brunner, A. Miraçi, D. Praetorius, J. Streitberger: Optimal complexity of goal-oriented adaptive FEM with nested iterative solvers, CMAM-10, Bonn, 12. Juni 2024 [slides]
P. Bringmann, M. Brunner, M. Feischl, A. Miraçi, D. Praetorius, J. Streitberger: 2fast2converge - Optimal complexity of adaptive FEM for second-order elliptic PDEs, PhD Colloquium of the Vienna School of Mathematics, Wien, 15. April 2024 [slides]
P. Bringmann, M. Brunner, A. Miraçi, D. Praetorius, J. Streitberger: Cost-optimal goal-oriented adaptive FEM for linear elliptic PDEs, ENUMATH 2023, Lisbon, Portugal, 04. September 2023 [slides]
M. Brunner, P. Heid, M. Innerberger, A. Miraçi, D. Praetorius, J. Streitberger: Adaptive FEM for linear elliptic PDEs: optimal complexity, 17th Austrian Numerical Analysis Day, Wien, 27.-28. April 2023 [slides]
M. Brunner, A. Miraçi, D. Praetorius, J. Streitberger: Optimal cost of AFEM for linear elliptic PDEs, 2nd SFB International Workshop 2023 "Taming Complexity in Partial Differential Systems", Wien, 19.-21. April 2023

Thesis: Optimal complexity of standard and goal-oriented adaptive FEM for general second-order linear elliptic PDEs [www], opens a file in a new window [slides], opens a file in a new window

Dissertation: Optimal complexity of standard and goal-oriented adaptive FEM for general second-order linear elliptic PDEs [www], opens a file in a new window [slides], opens a file in a new window

Poster pdf 1 MB , download

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ANID	Is needed to display Google ads on non-Google websites.	2 years	HTTP	Google AdSense
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DSID	Is needed by DoubleClick for advertising displayed in various places on the web and used to store the preferences of users.	2 years	HTTP	Doubleclick
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HSID	Contains the Google account ID and the last login time of the user.	2 years	HTTP	Google
IDE	Is needed by DoubleClick to record and report the actions of users on the website after viewing or clicking on one of the provider's ads, with the purpose of measuring the effectiveness of an advertisement and displaying targeted advertisements to users.	2 years	HTTP	Doubleclick
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SID	Contains the Google account ID and the last login time of the user.	2 years	HTTP	Google
SIDCC	Is needed to store information about user settings and information for Google Maps.	3 months	HTTP	Google
SSID	Is needed to collect visitor information for videos hosted by YouTube on Google Maps integrated maps.	persistent	HTTP	Google
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__SECURE-APISID	Is needed to profile the interests of website visitors in order to display relevant and personalized advertising through retargeting.	8 months	HTTP	Google
__SECURE-HSID	Is needed to secure digitally signed and encrypted data from the unique Google ID and to store the last login time that Google uses to identify visitors, prevent fraudulent use of login data, and protect visitor data from unauthorized parties. This may also be used for targeting purposes to display relevant and personalized advertising content.	8 months	HTTP	Google
__SECURE-SSID	Is needed to store information about how visitors use the site and about the ads they may have seen before visiting the site. Also used to customize ads on Google domains.	8 months	HTTP	Google
test_cookie	Is set as a test to check whether the browser allows cookies to be set. Does not contain any identification features.	15 minutes	HTTP	Google
VISITOR_INFO1_LIVE	Is needed by YouTube to store user settings and to calculate user bandwidth.	6 months	HTTP	Youtube
facebook	Is used to Enable ad delivery or retargeting	90 days	HTTP	Meta (Facebook)
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_fbc	Is needed to save the last visit (marketing/tracking).	2 years	HTTP	Meta (Facebook)
fbm	Is needed to store account data (marketing/tracking).	1 year	HTTP	Meta (Facebook)
xs	Is needed to store a unique session ID (marketing/tracking).	1 year	HTTP	Meta (Facebook)
wd	Is needed to log the screen resolution.	1 week	HTTP	Meta (Facebook)
fr	Is needed to serve ads and measure and improve their relevance.	3 months	HTTP	Meta (Facebook)
act	Is needed to store logged in users (marketing/tracking).	90 days	HTTP	Meta (Facebook)
_fbp	Is needed to store and track visits to various websites (marketing/tracking).	3 months	HTTP	Meta (Facebook)
datr	Is needed to identify the browser for security and website integrity purposes, including account recovery and identification of potentially compromised accounts.	2 years	HTTP	Meta (Facebook)
dpr	Is used for analysis purposes. Technical parameters are logged (e.g. aspect ratio and dimensions of the screen) so that Facebook apps can be displayed correctly.	1 week	HTTP	Meta (Facebook)
sb	Is needed to store browser details and security information of the Facebook account.	2 years	HTTP	Meta (Facebook)
dbln	Is needed to store browser details and security information of the Facebook account.	2 years	HTTP	Meta (Facebook)
spin	Is needed for promotional purposes and social campaign reporting.	session	HTTP	Meta (Facebook)
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cppo	Is needed for statistical purposes.	90 days	HTTP	Meta (Facebook)
locale	Is needed to save the language settings.	session	HTTP	Meta (Facebook)
pl	Required for Facebook Pixel.	2 years	HTTP	Meta (Facebook)
lu	Required for Facebook Pixel.	2 years	HTTP	Meta (Facebook)
c_user	Required for Facebook Pixel.	3 months	HTTP	Meta (Facebook)
bcookie	Is needed to store browser data (marketing/tracking).	2 years	HTTP	LinkedIn
li_oatml	Is needed to identify LinkedIn members outside of LinkedIn for advertising and analytics purposes.	1 month	HTTP	LinkedIn
BizographicsOptOut	Is needed to save privacy settings.	10 years	HTTP	LinkedIn
li_sugr	Is needed to store browser data (marketing/tracking).	3 months	HTTP	LinkedIn
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linkedin_oauth_	Is needed to provide cross-page functionality.	session	HTTP	LinkedIn
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lms_ads	Is needed to identify LinkedIn members outside of LinkedIn.	30 days	HTTP	LinkedIn
lms_analytics	Is needed to identify LinkedIn members for analytics purposes.	30 days	HTTP	LinkedIn
li_fat_id	Required for indirect member identification used for conversion tracking, retargeting and analytics.	30 days	HTTP	LinkedIn
U	Is needed to identify the browser.	3 months	HTTP	LinkedIn
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Current fields of research

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Thesis

Thesis