Geodesic
Explicit finite element error estimates for nonhomogeneous Neumann problems
Applications of Mathematics, Tome 63 (2018) no. 3, pp. 367-379.

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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 $0.5$.
DOI : 10.21136/AM.2018.0095-18
Classification : 65N15, 65N30
Keywords: finite element methods; nonhomogeneous Neumann problems; explicit error estimates 
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     author = {Li, Qin and Liu, Xuefeng},
     title = {Explicit finite element error estimates for nonhomogeneous {Neumann} problems},
     journal = {Applications of Mathematics},
     pages = {367--379},
     publisher = {mathdoc},
     volume = {63},
     number = {3},
     year = {2018},
     doi = {10.21136/AM.2018.0095-18},
     mrnumber = {3833665},
     zbl = {06945737},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.2018.0095-18/}
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Li, Qin; Liu, Xuefeng. Explicit finite element error estimates for nonhomogeneous Neumann problems. Applications of Mathematics, Tome 63 (2018) no. 3, pp. 367-379. doi : 10.21136/AM.2018.0095-18. http://geodesic.mathdoc.fr/articles/10.21136/AM.2018.0095-18/

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