Proves that the p-th order EERK method for semilinear parabolic problems with initial regularity γ achieves convergence rate min(1 + γ/2 + ρ1(γ)/2, p).
Thomée,Galerkin Finite Element Methods for Parabolic Problems, 2nd ed., Springer, Berlin
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Numerical tests indicate that a stochastic Galerkin discretization with embedded slabwise space-time finite elements and GMRES-GMG solvers outperforms Monte-Carlo sampling for random parabolic problems in convergence and algebraic solver statistics.
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Higher-order exponential Runge-Kutta Galerkin finite element method for semilinear parabolic problems with nonsmooth data
Proves that the p-th order EERK method for semilinear parabolic problems with initial regularity γ achieves convergence rate min(1 + γ/2 + ρ1(γ)/2, p).
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Stochastic Galerkin and Monte-Carlo methods for parabolic problems: Numerical performance of variational matrix-free approximations
Numerical tests indicate that a stochastic Galerkin discretization with embedded slabwise space-time finite elements and GMRES-GMG solvers outperforms Monte-Carlo sampling for random parabolic problems in convergence and algebraic solver statistics.