Space-time approximation of stochastic \(p\)-Laplace-type systems. (English) Zbl 1496.65156
Summary: We consider systems of stochastic evolutionary equations of \(p\)-Laplace type. We establish convergence rates for a finite-element-based space-time approximation, where the error is measured in a suitable quasi-norm. Under natural regularity assumptions on the solution, our main result provides linear convergence in space and convergence of order (almost) 1/2 in time. The key ingredient of our analysis is a random time-grid, which allows us to compensate for the lack of time regularity. Our theoretical results are confirmed by numerical experiments.
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N15 | Error bounds for boundary value problems involving PDEs |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
| 35K55 | Nonlinear parabolic equations |
| 35K65 | Degenerate parabolic equations |
| 35K92 | Quasilinear parabolic equations with \(p\)-Laplacian |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
Keywords:
parabolic stochastic PDEs; nonlinear Laplace-type systems; finite element methods; space-time discretizationReferences:
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