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math.NA2024
A posteriori error estimators for fourth order elliptic problems with concentrated loads
Huihui Cao, Yunqing Huang, Nianyu Yi +1
In this paper, we study two residual-based a posteriori error estimators for the interior penalty method in solving the biharmonic equation in a polygonal domain under a conc…
math.NA2024
A structure-preserving relaxation Crank-Nicolson finite element method for the Schrödinger-Poisson equation
Huini Liu, Nianyu Yi, Peimeng Yin
In this paper, we propose a mass- and modified energy-conservative relaxation Crank-Nicolson finite element method for the Schrödinger-Poisson equation. Utilizing only a single aux…
math.NA2024★ 1 cited
Unconditionally energy stable IEQ-FEMs for the Cahn-Hilliard equation and Allen-Cahn equation
Yaoyao Chen, Hailiang Liu, Nianyu Yi +1
In this paper, we present several unconditionally energy-stable invariant energy quadratization (IEQ) finite element methods (FEMs) with linear, first- and second-order accuracy fo…