@phdthesis{oai:niigata-u.repo.nii.ac.jp:02001012,
 author = {Nakano, Taiga and 中野, 泰河},
 month = {2023-05-24, 2023-05-24},
 note = {High-precision numerical methods are required to solve differential equations that govern physical models for measurement problems appearing in the semiconductor industry, in order to provide reliable and accurate measurement results. In the field of numerical analysis, recent studies are concerning on methods that provide guaranteed error estimation for numerical results obtained by finite element methods (FEM). In particular, Kikuchi and Liu have proposed the hypercircle based a posteriori and a priori error estimation. As required by the four-probe method for resistivity measurement, the local error estimation for FEM solutions of Poisson equations plays an important role in improving the precision of the measurement results. This study aims to extend the hypercircle method to estimate local errors for boundary value problems of the Poisson equation. Meanwhile, the application of the hypercircle method to the error estimation theory for the non-homogeneous Neumann boundary value problems of the modified Helmholtz equation is considered., 新大院博(理)第484号},
 school = {新潟大学, Niigata University},
 title = {Hypercircle-based local error estimation for the finite element solution of partial differential equations},
 year = {}
}