TY - JOUR T1 - $H^1$-Stability and Convergence of the FE, FV and FD Methods for an Elliptic Equation JO - East Asian Journal on Applied Mathematics VL - 2 SP - 154 EP - 170 PY - 2018 DA - 2018/02 SN - 3 DO - http://doi.org/10.4208/eajam.030513.200513a UR - https://global-sci.org/intro/article_detail/eajam/10853.html KW - Finite element method, finite difference method, finite volume method, Poisson equation, stability and convergence. AB -

We obtain the coefficient matrices of the finite element (FE), finite volume (FV) and finite difference (FD) methods based on $P_1$-conforming elements on a quasi-uniform mesh, in order to approximately solve a boundary value problem involving the elliptic Poisson equation. The three methods are shown to possess the same $H^1$-stability and convergence. Some numerical tests are made, to compare the numerical results from the three methods and to review our theoretical results.