SIAM Journal on Numerical Analysis · 2012 · 62 citations · 7 references
ComputingComputational EngineeringPhysicsComputational MechanicsFinite Element AnalysisFinite Element MethodsError EstimationFinite Element DiscretizationFinite Element FormulationNonlinear Finite Element AnalysisNumerical AlgorithmsNumerical Methods For Differential EquationsError Estimation For Finite Element SolutionsFinite Element Modeling
The nonlocal term in the nonlinear equations of Kirchhoff type causes difficulties when the equation is solved numerically by using the Newton–Raphson method. This is because the Jacobian of the Newton–Raphson method is full. In this article, the finite element system is replaced by an equivalent system for which the Jacobian is sparse. We derive quasi-optimal error estimates for the finite element method and demonstrate the results with numerical experiments.
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