@Article{EAJAM-3-154, author = {}, title = {$H^1$-Stability and Convergence of the FE, FV and FD Methods for an Elliptic Equation}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {3}, number = {2}, pages = {154--170}, abstract = {

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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.030513.200513a }, url = {http://global-sci.org/intro/article_detail/eajam/10853.html} }