{"intvolume":"        13","language":[{"iso":"eng"}],"page":"1287-1313","date_updated":"2024-04-29T12:21:56Z","abstract":[{"text":"Based on approximation of the balance equation, finite difference schemes on triangular cell-centered grids are derived. A priori estimates and error analyses are provided. For certain regular triangulations, convergence in the discrete -norm is established. Also, finite difference schemes on triangular cell-centered grids with local refinement are derived with accuracy , where for a simple symmetric scheme, for a nonsymmetric and a more accurate symmetric scheme, and\r\nfor a more accurate nonsymmetric scheme.\r\nCertain algebraic properties of the corresponding matrices of the derived finite difference schemes are verified, thus allowing the recently proposed algebraic theory for the Bramble–Ewing–Pasciak–Schatz (BEPS) and Fact Adaptive Composite (FAC) two-grid preconditioners to apply.\r\nNumerical experiments that demonstrate the accuracy of the difference schemes and the fast convergence of the two-grid BEPS and FAC preconditioners in conjugate gradient-type iterative methods are presented.","lang":"eng"}],"publication_identifier":{"eissn":["2168-3417"],"issn":["0196-5204"]},"type":"journal_article","volume":13,"doi":"10.1137/0913073","author":[{"first_name":"P. S.","full_name":"Vassilevski, P. S.","last_name":"Vassilevski"},{"first_name":"Svetozara","id":"201871","full_name":"Petrova, Svetozara","last_name":"Petrova"},{"first_name":"R. D.","last_name":"Lazarov","full_name":"Lazarov, R. D."}],"issue":"6","publisher":"Society for Industrial & Applied Mathematics (SIAM)","status":"public","_id":"4546","user_id":"220548","citation":{"ama":"Vassilevski PS, Petrova S, Lazarov RD. Finite Difference Schemes on Triangular Cell-Centered Grids with Local Refinement. <i>SIAM Journal on Scientific and Statistical Computing</i>. 1992;13(6):1287-1313. doi:<a href=\"https://doi.org/10.1137/0913073\">10.1137/0913073</a>","mla":"Vassilevski, P. S., et al. “Finite Difference Schemes on Triangular Cell-Centered Grids with Local Refinement.” <i>SIAM Journal on Scientific and Statistical Computing</i>, vol. 13, no. 6, Society for Industrial &#38; Applied Mathematics (SIAM), 1992, pp. 1287–313, doi:<a href=\"https://doi.org/10.1137/0913073\">10.1137/0913073</a>.","bibtex":"@article{Vassilevski_Petrova_Lazarov_1992, title={Finite Difference Schemes on Triangular Cell-Centered Grids with Local Refinement}, volume={13}, DOI={<a href=\"https://doi.org/10.1137/0913073\">10.1137/0913073</a>}, number={6}, journal={SIAM Journal on Scientific and Statistical Computing}, publisher={Society for Industrial &#38; Applied Mathematics (SIAM)}, author={Vassilevski, P. S. and Petrova, Svetozara and Lazarov, R. D.}, year={1992}, pages={1287–1313} }","apa":"Vassilevski, P. S., Petrova, S., &#38; Lazarov, R. D. (1992). Finite Difference Schemes on Triangular Cell-Centered Grids with Local Refinement. <i>SIAM Journal on Scientific and Statistical Computing</i>, <i>13</i>(6), 1287–1313. <a href=\"https://doi.org/10.1137/0913073\">https://doi.org/10.1137/0913073</a>","chicago":"Vassilevski, P. S., Svetozara Petrova, and R. D. Lazarov. “Finite Difference Schemes on Triangular Cell-Centered Grids with Local Refinement.” <i>SIAM Journal on Scientific and Statistical Computing</i> 13, no. 6 (1992): 1287–1313. <a href=\"https://doi.org/10.1137/0913073\">https://doi.org/10.1137/0913073</a>.","ieee":"P. S. Vassilevski, S. Petrova, and R. D. Lazarov, “Finite Difference Schemes on Triangular Cell-Centered Grids with Local Refinement,” <i>SIAM Journal on Scientific and Statistical Computing</i>, vol. 13, no. 6, pp. 1287–1313, 1992.","alphadin":"<span style=\"font-variant:small-caps;\">Vassilevski, P. S.</span> ; <span style=\"font-variant:small-caps;\">Petrova, Svetozara</span> ; <span style=\"font-variant:small-caps;\">Lazarov, R. D.</span>: Finite Difference Schemes on Triangular Cell-Centered Grids with Local Refinement. In: <i>SIAM Journal on Scientific and Statistical Computing</i> Bd. 13, Society for Industrial &#38; Applied Mathematics (SIAM) (1992), Nr. 6, S. 1287–1313","short":"P.S. Vassilevski, S. Petrova, R.D. Lazarov, SIAM Journal on Scientific and Statistical Computing 13 (1992) 1287–1313."},"publication":"SIAM Journal on Scientific and Statistical Computing","date_created":"2024-04-25T12:57:40Z","title":"Finite Difference Schemes on Triangular Cell-Centered Grids with Local Refinement","project":[{"name":"Institute for Data Science Solutions","_id":"f432a2ee-bceb-11ed-a251-a83585c5074d"}],"year":"1992","publication_status":"published"}