Finite element analysisDisplacementErrorsGridsConvergenceBoundary value problemsMeshPeriodic functionsSuperconvergenceApproximationIn this paper we introduce a new definition of superconvergence - the n%-superconvergence, which generalizes the classical idea of superconvergence to general meshes. We show that this ...
By the definition of Qρ1, we obtain (27)‖u−Qρ1uh‖0≤‖u−Qρ1u‖0+‖Qρ1u−Qρ1uh‖0≤C(ρ1s+1‖u‖s+1+h2(‖u‖2+‖p‖1+‖f‖1))≤C(hσ1(s+1)‖u‖s+1+h2(‖u‖2+‖p‖1+‖f‖1)). The above error estimate can be optimized by choosing σ1=2s+1...
According to the definition of [Math Processing Error]Rh, we get [Math Processing Error](dtRhyn−dtyhn,wh)+a(Rhyn−yhn,wh)+(un(Rhyn−yhn),wh)=(dtRhyn−dtyn+dtyn−ytn+un(Rhyn−yn)+yhn(uhn−un),wh). (48) Note that [Math Processing Error](dtRhyn−dtyhn,Rhyn−...
Definition 4.1 We assume that two Numerical examples In order to examine the performance of our new Hermite-type triangular element, we consider two examples of problem (2.1) with Ω=[0,1]2 and f=-▵u, where u1(x,y)=(1-e-yε)x(1-x)(1-y), ε=0.05 and u2(x,y)=xy(1-x)...