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Explicit finite element error estimates for nonhomogeneous Neumann problems

Qin Li;  Xuefeng Liu — 2018

Applications of Mathematics

The paper develops an explicit a priori error estimate for finite element solution to nonhomogeneous Neumann problems. For this purpose, the hypercircle over finite element spaces is constructed and the explicit upper bound of the constant in the trace theorem is given. Numerical examples are shown in the final section, which implies the proposed error estimate has the convergence rate as 0 . 5 .

Explicit estimation of error constants appearing in non-conforming linear triangular finite element method

Xuefeng Liu;  Fumio Kikuchi — 2018

Applications of Mathematics

The non-conforming linear ( P 1 ) triangular FEM can be viewed as a kind of the discontinuous Galerkin method, and is attractive in both the theoretical and practical purposes. Since various error constants must be quantitatively evaluated for its accurate a priori and a posteriori error estimates, we derive their theoretical upper bounds and some computational results. In particular, the Babuška-Aziz maximum angle condition is required just as in the case of the conforming P 1 triangle. Some applications...

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