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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 84, 2012 - Issue 2-3: Stochastic Analysis: papers from the International Conference on Stochastic Analysis and Applications, October 12–17, 2009. Hammamet, Tunisi
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Original Articles

Simulation of stochastic partial differential equations using finite element methods

Andrea Barth Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern, N-0316, Oslo, NorwayCorrespondence[email protected]
&
Annika Lang Fakultät Für Mathematik und Informatik, Universität Mannheim, D-68131, Mannheim, Germany
Pages 217-231 | Received 01 Mar 2010, Accepted 09 Sep 2010, Published online: 09 Jun 2011

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Andrea Barth & Fred Espen Benth. (2014) The forward dynamics in energy markets – infinite-dimensional modelling and simulation. Stochastics 86:6, pages 932-966.
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Andrea Barth & Annika Lang. (2012) Multilevel Monte Carlo method with applications to stochastic partial differential equations. International Journal of Computer Mathematics 89:18, pages 2479-2498.
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Articles from other publishers (38)

Raffaele D’Ambrosio & Stefano Di Giovacchino. (2023) Numerical conservation issues for the stochastic Korteweg–de Vries equation. Journal of Computational and Applied Mathematics 424, pages 114967.
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Mahdi Jalili, Rezvan Salehi & Mehdi Dehghan. (2023) An efficient meshless method to approximate semi-linear stochastic evolution equations. Engineering with Computers.
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Andrea Barth & Andreas Stein. (2022) Numerical analysis for time-dependent advection-diffusion problems with random discontinuous coefficients. ESAIM: Mathematical Modelling and Numerical Analysis 56:5, pages 1545-1578.
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Wanyang Dai. (2022) Convolutional neural network based simulation and analysis for backward stochastic partial differential equations. Computers & Mathematics with Applications 119, pages 21-58.
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Fred Espen Benth, Nils Detering & Silvia Lavagnini. (2021) Accuracy of deep learning in calibrating HJM forward curves. Digital Finance 3:3-4, pages 209-248.
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Annika Lang. 2021. Computer Vision. Computer Vision 1212 1217 .
Annika Lang. 2020. Computer Vision. Computer Vision 1 6 .
Christoph Reisinger & Yufei Zhang. (2020) Rectified deep neural networks overcome the curse of dimensionality for nonsmooth value functions in zero-sum games of nonlinear stiff systems. Analysis and Applications 18:06, pages 951-999.
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Rikard Anton, David Cohen & Lluis Quer-Sardanyons. (2020) A fully discrete approximation of the one-dimensional stochastic heat equation. IMA Journal of Numerical Analysis 40:1, pages 247-284.
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Jean Daniel Mukam & Antoine Tambue. (2019) Optimal strong convergence rates of numerical methods for semilinear parabolic SPDE driven by Gaussian noise and Poisson random measure. Computers & Mathematics with Applications 77:10, pages 2786-2803.
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Xu Yang & Weidong Zhao. (2018) Finite element methods and their error analysis for SPDEs driven by Gaussian and non-Gaussian noises. Applied Mathematics and Computation 332, pages 58-75.
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Mahboub Baccouch. (2018) A stochastic local discontinuous Galerkin method for stochastic two-point boundary-value problems driven by additive noises. Applied Numerical Mathematics 128, pages 43-64.
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Andrea Barth & Andreas Stein. (2017) Approximation and simulation of infinite-dimensional Lévy processes. Stochastics and Partial Differential Equations: Analysis and Computations 6:2, pages 286-334.
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Martin Neumüller & Andreas Thalhammer. (2018) A Fully Parallelizable Space-Time Multilevel Monte Carlo Method for Stochastic Differential Equations with Additive Noise. SIAM Journal on Scientific Computing 40:3, pages C388-C400.
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Martin Redmann. (2018) Type II Singular Perturbation Approximation for Linear Systems with Lévy Noise. SIAM Journal on Control and Optimization 56:3, pages 2120-2158.
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Annika Lang & Andreas Petersson. (2018) Monte Carlo versus multilevel Monte Carlo in weak error simulations of SPDE approximations. Mathematics and Computers in Simulation 143, pages 99-113.
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Andrea Barth & Tobias Stüwe. (2018) Weak convergence of Galerkin approximations of stochastic partial differential equations driven by additive Lévy noise. Mathematics and Computers in Simulation 143, pages 215-225.
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Martin Neumüller & Andreas Thalhammer. 2018. Domain Decomposition Methods in Science and Engineering XXIV. Domain Decomposition Methods in Science and Engineering XXIV 493 501 .
Annika Lang, Andreas Petersson & Andreas Thalhammer. (2017) Mean-square stability analysis of approximations of stochastic differential equations in infinite dimensions. BIT Numerical Mathematics 57:4, pages 963-990.
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Hacer Öz Bakan, Fikriye Yılmaz & Gerhard-Wilhelm Weber. (2017) A discrete optimality system for an optimal harvesting problem. Computational Management Science 14:4, pages 519-533.
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Robert Altmann, Tijana Levajković & Hermann Mena. (2016) Operator differential-algebraic equations with noise arising in fluid dynamics. Monatshefte für Mathematik 182:4, pages 741-780.
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Zhongqiang Zhang & George Em KarniadakisZhongqiang Zhang & George Em Karniadakis. 2017. Numerical Methods for Stochastic Partial Differential Equations with White Noise. Numerical Methods for Stochastic Partial Differential Equations with White Noise 53 97 .
Fikriye Yılmaz, Hacer Öz Bakan & Gerhard-Wilhelm Weber. 2017. Modeling, Dynamics, Optimization and Bioeconomics II. Modeling, Dynamics, Optimization and Bioeconomics II 513 532 .
Andrea Barth, Christoph Schwab & Jonas Šukys. 2016. Monte Carlo and Quasi-Monte Carlo Methods. Monte Carlo and Quasi-Monte Carlo Methods 209 227 .
Annika Lang. 2016. Monte Carlo and Quasi-Monte Carlo Methods. Monte Carlo and Quasi-Monte Carlo Methods 489 505 .
Bohan Chen, Carsten Chong & Claudia Klüppelberg. 2016. The Fascination of Probability, Statistics and their Applications. The Fascination of Probability, Statistics and their Applications 209 229 .
Mehdi Dehghan & Mohammad Shirzadi. (2016) A meshless method based on the dual reciprocity method for one-dimensional stochastic partial differential equations. Numerical Methods for Partial Differential Equations 32:1, pages 292-306.
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Mehdi Dehghan & Mohammad Shirzadi. (2015) The modified dual reciprocity boundary elements method and its application for solving stochastic partial differential equations. Engineering Analysis with Boundary Elements 58, pages 99-111.
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Mehdi Dehghan & Mohammad Shirzadi. (2015) Meshless simulation of stochastic advection–diffusion equations based on radial basis functions. Engineering Analysis with Boundary Elements 53, pages 18-26.
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Mihály Kovács, Felix Lindner & René L. Schilling. (2015) Weak Convergence of Finite Element Approximations of Linear Stochastic Evolution Equations with Additive Lévy Noise. SIAM/ASA Journal on Uncertainty Quantification 3:1, pages 1159-1199.
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Christoph Schwab. 2015. Encyclopedia of Applied and Computational Mathematics. Encyclopedia of Applied and Computational Mathematics 903 913 .
Ralf Kornhuber, Christoph Schwab & Maren-Wanda Wolf. (2014) Multilevel Monte Carlo Finite Element Methods for Stochastic Elliptic Variational Inequalities. SIAM Journal on Numerical Analysis 52:3, pages 1243-1268.
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Annika Lang. 2014. Computer Vision. Computer Vision 770 775 .
Andrea Barth & Annika Lang. (2013) and almost sure convergence of a Milstein scheme for stochastic partial differential equations . Stochastic Processes and their Applications 123:5, pages 1563-1587.
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Andrea Barth, Annika Lang & Christoph Schwab. (2012) Multilevel Monte Carlo method for parabolic stochastic partial differential equations. BIT Numerical Mathematics 53:1, pages 3-27.
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Assyr Abdulle, Andrea Barth & Christoph Schwab. (2013) Multilevel Monte Carlo Methods for Stochastic Elliptic Multiscale PDEs. Multiscale Modeling & Simulation 11:4, pages 1033-1070.
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Andrea Barth & Annika Lang. (2012) Milstein Approximation for Advection-Diffusion Equations Driven by Multiplicative Noncontinuous Martingale Noises. Applied Mathematics & Optimization 66:3, pages 387-413.
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Annika Lang. (2012) Almost sure convergence of a Galerkin approximation for SPDEs of Zakai type driven by square integrable martingales. Journal of Computational and Applied Mathematics 236:7, pages 1724-1732.
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