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We consider Galerkin finite element methods for semilinear stochastic partial differential equations (SPDEs) with multiplicative noise and Lipschitz continuous nonlinearities.
The maximum rate of convergence of discrete approximations for stochastic differential equations
J. M. C. Clark and R. J. Cameron · 1980
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Geometric Theory of Semilinear Parabolic Equations
D. Henry · 1981
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Semigroups of Linear Operators and Applications to Partial Differential Equations
A. Pazy · 1983
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The stability in L p L_{p} and W p 1 W^{1}_{p} of the L 2 L_{2} -projection onto finite element function spaces
M. Crouzeix and V. Thomée · 1987
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Stochastic Equations in Infinite Dimensions
G. Da Prato and J. Zabczyk · 1992
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Error estimates with smooth and nonsmooth data for a finite element method for the Cahn-Hilliard equation
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On the discretization in time of parabolic stochastic partial differential equations
J. Printems · 2001
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Merging the Bramble-Pasciak-Steinbach and the Crouzeix-Thomée criterion for H 1 H^{1} -stability of the L 2 L^{2} -projection onto finite element spaces
C. Carstensen · 2002
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Error estimates for semidiscrete finite element approximations of linear and semilinear parabolic equations under minimal regularity assumptions
K. Chrysafinos and L. S. Hou · 2002
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Approximation for semilinear stochastic evolution equations
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An adaptive mesh-refining algorithm allowing for an H 1 H^{1} stable L 2 L^{2} projection onto Courant finite element spaces
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Semidiscrete Galerkin approximation for a linear stochastic parabolic partial differential equation driven by an additive noise
Y. Yan · 2004
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Y. Yan · 2005
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Spectral Methods for Time-Dependent Problems
Weak order for the discretization of the stochastic heat equation
A. Debussche and J. Printems · 2009
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Rate of weak convergence of the finite element method for the stochastic heat equation with additive noise
M. Geissert, M. Kovács, and S. Larsson · 2009
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The numerical approximation of stochastic partial differential equations
A. Jentzen and P. E. Kloeden · 2009
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Weak approximation of the stochastic wave equation
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A. Jentzen and M. Röckner · 2010
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Strong convergence of the finite element method with truncated noise for semilinear parabolic stochastic equations with additive noise
M. Kovács, S. Larsson, and F. Lindgren · 2010
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Optimal regularity for semilinear stochastic partial differential equations with multiplicative noise
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Weak approximation of stochastic partial differential equations: the nonlinear case
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