A note on exponential Rosenbrock-Euler method for the finite element discretization of a semilinear parabolic partial differential equation

DOI10.1016/j.camwa.2018.07.025zbMath1434.65188arXiv1610.05525OpenAlexW2963535445WikidataQ115359503 ScholiaQ115359503MaRDI QIDQ2293593

Jean Daniel Mukam, Antoine Tambue

Publication date: 5 February 2020

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.05525

zbMATH Keywords

finite element methodparabolic partial differential equationerrors estimateexponential Rosenbrock-type methodssmooth \& nonsmooth initial data

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Semilinear parabolic equations (35K58)

Related Items (8)

A high-order exponential integrator for nonlinear parabolic equations with nonsmooth initial data ⋮ Strong convergence of a stochastic Rosenbrock-type scheme for the finite element discretization of semilinear SPDEs driven by multiplicative and additive noise ⋮ Magnus-type integrator for non-autonomous SPDEs driven by multiplicative noise ⋮ A combined meshfree exponential Rosenbrock integrator for the third‐order dispersive partial differential equations ⋮ Weak convergence of the finite element method for semilinear parabolic SPDEs driven by additive noise ⋮ Optimal strong convergence rates of numerical methods for semilinear parabolic SPDE driven by Gaussian noise and Poisson random measure ⋮ Optimal strong convergence rates of some Euler-type timestepping schemes for the finite element discretization SPDEs driven by additive fractional Brownian motion and Poisson random measure ⋮ Optimal error estimate of the finite element approximation of second order semilinear non-autonomous parabolic PDEs

Cites Work

• Unnamed Item
• Unnamed Item
• Optimal regularity for semilinear stochastic partial differential equations with multiplicative noise
• Weak convergence for a stochastic exponential integrator and finite element discretization of stochastic partial differential equation with multiplicative \& additive noise
• A class of explicit multistep exponential integrators for semilinear problems
• Strong convergence of the finite element method with truncated noise for semilinear parabolic stochastic equations with additive noise
• Exponential Rosenbrock integrators for option pricing
• Implementation of exponential Rosenbrock-type integrators
• Semigroups of linear operators and applications to partial differential equations
• Geometric theory of semilinear parabolic equations
• Convergence of Runge-Kutta methods for nonlinear parabolic equations
• Strong convergence analysis of the stochastic exponential Rosenbrock scheme for the finite element discretization of semilinear SPDEs driven by multiplicative and additive noise
• An exponential integrator for finite volume discretization of a reaction-advection-diffusion equation
• A class of explicit exponential general linear methods
• Backward Euler discretization of fully nonlinear parabolic problems
• Weak convergence for a spatial approximation of the nonlinear stochastic heat equation
• Exponential integrators
• An Introduction to Computational Stochastic PDEs
• A note on the Zassenhaus product formula
• An efficient algorithm for computing the Baker–Campbell–Hausdorff series and some of its applications
• On the Discretization in Time of Semilinear Parabolic Equations with Nonsmooth Initial Data
• Error Estimates for Spatially Discrete Approximations of Semilinear Parabolic Equations with Nonsmooth Initial Data
• Non-smooth data error estimates for linearly implicit Runge-Kutta methods
• Stochastic exponential integrators for the finite element discretization of SPDEs for multiplicative and additive noise
• Exponential Rosenbrock-Type Methods
• Optimal error estimates of Galerkin finite element methods for stochastic partial differential equations with multiplicative noise
• Galerkin Finite Element Methods for Parabolic Problems
• Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems
• On the exponential solution of differential equations for a linear operator
• Runge-Kutta time discretization of reaction-diffusion and Navier-Stokes equations: Nonsmooth-data error estimates and applications to long-time behaviour

This page was built for publication: A note on exponential Rosenbrock-Euler method for the finite element discretization of a semilinear parabolic partial differential equation