SIAM Journal on Numerical Analysis · 2009 · 19 citations · 4 references
EngineeringComputational EngineeringMechanical EngineeringComputational MechanicsFinite Element AnalysisFinite Element MethodsConvergence AnalysisFinite Element DiscretizationFinite Element FormulationMonte Carlo MethodsMonte Carlo SimulationStochastic Differential EquationsFinite Element Methods In AcousticsFinite Element ModelingFinite Element SimulationNumerical Methods For Stochastic Differential EquationsNumerical Solutions Of Partial Differential Equations
An efficient method for obtaining numerical solutions of an elasto-plastic oscillator with noise is considered. Since Monte Carlo simulations for the underlying stochastic process are too slow, as an alternative, approximate solutions of the partial differential equation defining the invariant measure of the process are studied. The regularity of the solution of that partial differential equation is not sufficient to employ a “standard” finite element method. To overcome the difficulty, an ultra weak finite element method has been developed and successfully implemented.
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