Stochastic exponential integrators for the finite element discretization of SPDEs for multiplicative and additive noise

IMA Journal of Numerical Analysis ◽

10.1093/imanum/drr059 ◽

2012 ◽

Vol 33 (2) ◽

pp. 515-543 ◽

Author(s):

G. J. Lord ◽

A. Tambue

Keyword(s):

Finite Element ◽

Additive Noise ◽

Finite Element Discretization ◽

Exponential Integrators ◽

Element Discretization

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Strong Convergence Analysis of the Stochastic Exponential Rosenbrock Scheme for the Finite Element Discretization of Semilinear SPDEs Driven by Multiplicative and Additive Noise

Journal of Scientific Computing ◽

10.1007/s10915-017-0475-y ◽

2017 ◽

Vol 74 (2) ◽

pp. 937-978 ◽

Author(s):

Jean Daniel Mukam ◽

Antoine Tambue

Keyword(s):

Finite Element ◽

Strong Convergence ◽

Convergence Analysis ◽

Additive Noise ◽

Finite Element Discretization ◽

Element Discretization

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Strong convergence rates of the linear implicit Euler method for the finite element discretization of SPDEs with additive noise

IMA Journal of Numerical Analysis ◽

10.1093/imanum/drw016 ◽

2016 ◽

pp. drw016 ◽

Author(s):

Xiaojie Wang

Keyword(s):

Finite Element ◽

Strong Convergence ◽

Additive Noise ◽

Convergence Rates ◽

Euler Method ◽

Finite Element Discretization ◽

Element Discretization ◽

Implicit Euler Method ◽

Strong Convergence Rates

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A modified semi–implicit Euler–Maruyama scheme for finite element discretization of SPDEs with additive noise

Applied Mathematics and Computation ◽

10.1016/j.amc.2018.03.014 ◽

2018 ◽

Vol 332 ◽

pp. 105-122 ◽

Author(s):

Gabriel J. Lord ◽

Antoine Tambue

Keyword(s):

Finite Element ◽

Additive Noise ◽

Finite Element Discretization ◽

Element Discretization

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Strong convergence of the linear implicit Euler method for the finite element discretization of semilinear SPDEs driven by multiplicative or additive noise

Applied Mathematics and Computation ◽

10.1016/j.amc.2018.09.073 ◽

2019 ◽

Vol 346 ◽

pp. 23-40

Author(s):

Antoine Tambue ◽

Jean Daniel Mukam

Keyword(s):

Finite Element ◽

Strong Convergence ◽

Additive Noise ◽

Euler Method ◽

Finite Element Discretization ◽

Element Discretization ◽

Implicit Euler Method

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Strong convergence of a stochastic Rosenbrock-type scheme for the finite element discretization of semilinear SPDEs driven by multiplicative and additive noise

Stochastic Processes and their Applications ◽

10.1016/j.spa.2020.02.008 ◽

2020 ◽

Vol 130 (8) ◽

pp. 4968-5005

Author(s):

Jean Daniel Mukam ◽

Antoine Tambue

Keyword(s):

Finite Element ◽

Strong Convergence ◽

Additive Noise ◽

Finite Element Discretization ◽

Element Discretization

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Strong convergence of the linear implicit Euler method for the finite element discretization of semilinear non-autonomous SPDEs driven by multiplicative or additive noise

Applied Numerical Mathematics ◽

10.1016/j.apnum.2019.08.009 ◽

2020 ◽

Vol 147 ◽

pp. 222-253

Author(s):

Jean Daniel Mukam ◽

Antoine Tambue

Keyword(s):

Finite Element ◽

Strong Convergence ◽

Additive Noise ◽

Euler Method ◽

Finite Element Discretization ◽

Element Discretization ◽

Implicit Euler Method

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Weak convergence for a stochastic exponential integrator and finite element discretization of stochastic partial differential equation with multiplicative & additive noise

Applied Numerical Mathematics ◽

10.1016/j.apnum.2016.04.013 ◽

2016 ◽

Vol 108 ◽

pp. 57-86 ◽

Author(s):

Antoine Tambue ◽

Jean Medard T. Ngnotchouye

Keyword(s):

Differential Equation ◽

Partial Differential Equation ◽

Finite Element ◽

Weak Convergence ◽

Additive Noise ◽

Stochastic Partial Differential Equation ◽

Finite Element Discretization ◽

Partial Differential ◽

Element Discretization ◽

Exponential Integrator

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An adaptive BDDC preconditioner for advection-diffusion problems with a stabilized finite element discretization

Applied Numerical Mathematics ◽

10.1016/j.apnum.2021.02.012 ◽

2021 ◽

Vol 165 ◽

pp. 184-197

Author(s):

Jie Peng ◽

Shi Shu ◽

Junxian Wang ◽

Liuqiang Zhong

Keyword(s):

Finite Element ◽

Finite Element Discretization ◽

Element Discretization ◽

Stabilized Finite Element ◽

Advection Diffusion ◽

Diffusion Problems

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Two grid finite element discretization method for semi‐linear hyperbolic integro‐differential equations

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22370 ◽

2019 ◽

Vol 35 (5) ◽

pp. 1676-1693

Author(s):

Luoping Chen ◽

Yanping Chen ◽

Yunqing Huang

Keyword(s):

Finite Element ◽

Differential Equations ◽

Discretization Method ◽

Finite Element Discretization ◽

Element Discretization

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A Discontinuous Phase-Space Finite Element Discretization of the Linear Boltzmann-Vlasov Equation for Charged Particle Transport

Journal of Computational and Theoretical Transport ◽

10.1080/00411450.2014.910230 ◽

2014 ◽

Vol 43 (1-7) ◽

pp. 128-147 ◽

Author(s):

Shawn D. Pautz ◽

Clif Drumm ◽

Wesley C. Fan ◽

C. David Turner

Keyword(s):

Finite Element ◽

Charged Particle ◽

Phase Space ◽

Vlasov Equation ◽

Particle Transport ◽

Finite Element Discretization ◽

Element Discretization ◽

Discontinuous Phase ◽

Charged Particle Transport

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