We present a posteriori error estimator strategies for the leastsquares finite element method (LS) to approximate the exponential PhanThienTanner (PTT) viscoelastic fluid flows. The error estimator provides adaptive mass weights and mesh refinement criteria for improving LS solutions using lowerorder basis functions and a small number of elements. We analyze an a priori error estimate for the firstorder linearized LS system and show that the estimate is supported by numerical results. The LS approach is numerically tested for a convergence study and then applied to the flow past a slot channel. Numerical results verify that the proposed approach improves numerical solutions and resolves computational difficulties related to the presence of corner singularities and limitations arising from the exorbitant number of unknowns.
Citation: HsuehChen Lee, Hyesuk Lee. An a posteriori error estimator based on leastsquares finite element solutions for viscoelastic fluid flows[J]. Electronic Research Archive, 2021, 29(4): 27552770. doi: 10.3934/era.2021012
Abstract
We present a posteriori error estimator strategies for the leastsquares finite element method (LS) to approximate the exponential PhanThienTanner (PTT) viscoelastic fluid flows. The error estimator provides adaptive mass weights and mesh refinement criteria for improving LS solutions using lowerorder basis functions and a small number of elements. We analyze an a priori error estimate for the firstorder linearized LS system and show that the estimate is supported by numerical results. The LS approach is numerically tested for a convergence study and then applied to the flow past a slot channel. Numerical results verify that the proposed approach improves numerical solutions and resolves computational difficulties related to the presence of corner singularities and limitations arising from the exorbitant number of unknowns.
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