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\n We present formulations of the Trotter-Kato theorem for approximation of linear C\n \n \n \n \n \n 0<\/mml:mn>\n <\/mml:msub>\n {}_0<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n -semigroups which provide very useful framework when convergence of numerical approximations to solutions of PDEs are studied. Applicability of our results is demonstrated using a first order hyperbolic equation, a wave equation and Stokes\u2019 equation as illustrative examples.\n <\/p>","DOI":"10.1090\/s0025-5718-98-00915-6","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:44Z","timestamp":1027707284000},"page":"21-44","source":"Crossref","is-referenced-by-count":52,"title":["The Trotter-Kato theorem and approximation of PDEs"],"prefix":"10.1090","volume":"67","author":[{"given":"Kazufumi","family":"Ito","sequence":"first","affiliation":[]},{"given":"Franz","family":"Kappel","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1998]]},"reference":[{"issue":"1","key":"1","first-page":"73","article-title":"A unified framework for approximation in inverse problems for distributed parameter systems","volume":"4","author":"Banks, H. T.","year":"1988","journal-title":"Control Theory Adv. 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