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@ARTICLE{Clausnitzer:1014779,
      author       = {Clausnitzer, Julian and Kleefeld, Andreas},
      title        = {{A} spectral {G}alerkin exponential {E}uler time-stepping
                      scheme for parabolic {SPDE}s on two-dimensional domains with
                      a $\mathcal{{C}}^2$ boundary},
      journal      = {Discrete and continuous dynamical systems / Series B},
      volume       = {29},
      number       = {4},
      issn         = {1531-3492},
      address      = {Springfield, Mo.},
      publisher    = {American Institute of Mathematical Sciences},
      reportid     = {FZJ-2023-03463},
      pages        = {1624-1651},
      year         = {2024},
      abstract     = {We consider the numerical approximation of second-order
                      semi-linear parabolic stochastic partial differential
                      equations interpreted in the mild sense which we solve on
                      general two-dimensional domains with a boundary with
                      homogeneous Dirichlet boundary conditions. The equations are
                      driven by Gaussian additive noise, and several
                      Lipschitz-like conditions are imposed on the nonlinear
                      function. We discretize in space with a spectral Galerkin
                      method and in time using an explicit Euler-like scheme. For
                      irregular shapes, the necessary Dirichlet eigenvalues and
                      eigenfunctions are obtained from a boundary integral
                      equation method. This yields a nonlinear eigenvalue problem,
                      which is discretized using a boundary element collocation
                      method and is solved with the Beyn contour integral
                      algorithm. We present an error analysis as well as numerical
                      results on an exemplary asymmetric shape, and point out
                      limitations of the approach.},
      cin          = {JSC},
      ddc          = {510},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {5112 - Cross-Domain Algorithms, Tools, Methods Labs (ATMLs)
                      and Research Groups (POF4-511)},
      pid          = {G:(DE-HGF)POF4-5112},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:001122959000001},
      doi          = {10.3934/dcdsb.2023148},
      url          = {https://juser.fz-juelich.de/record/1014779},
}