{"title":"反扩散方程的离散分析","authors":"M. Breuß","doi":"10.1163/157404006778330861","DOIUrl":null,"url":null,"abstract":"We discuss some important issues arising when approximating numerically stabilised inverse diffusion processes. We prove rigorously the necessity of a minmod-type stabilisation. Furthermore, we give rigorously verified assertions concerning the occurence of undesirable staircasing aka terracing artefacts. The theoretical results are supplemented by numerical tests.","PeriodicalId":101169,"journal":{"name":"Soft Computing Letters","volume":"80 1","pages":"117-129"},"PeriodicalIF":0.0000,"publicationDate":"2006-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"An analysis of discretisations of inverse diffusion equations\",\"authors\":\"M. Breuß\",\"doi\":\"10.1163/157404006778330861\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We discuss some important issues arising when approximating numerically stabilised inverse diffusion processes. We prove rigorously the necessity of a minmod-type stabilisation. Furthermore, we give rigorously verified assertions concerning the occurence of undesirable staircasing aka terracing artefacts. The theoretical results are supplemented by numerical tests.\",\"PeriodicalId\":101169,\"journal\":{\"name\":\"Soft Computing Letters\",\"volume\":\"80 1\",\"pages\":\"117-129\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-03-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Soft Computing Letters\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1163/157404006778330861\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Soft Computing Letters","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1163/157404006778330861","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
An analysis of discretisations of inverse diffusion equations
We discuss some important issues arising when approximating numerically stabilised inverse diffusion processes. We prove rigorously the necessity of a minmod-type stabilisation. Furthermore, we give rigorously verified assertions concerning the occurence of undesirable staircasing aka terracing artefacts. The theoretical results are supplemented by numerical tests.
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