{"product_id":"a-numerical-method-for-anisotropic-elliptic-boundary-value-problems-von-miguel-dumett","title":"A Numerical Method for Anisotropic Elliptic Boundary Value Problems","description":"\u003cp\u003eWe present a new second-order stable Cartesian grid algorithm for  solving anisotropic elliptic boundary value problems on bounded  irregular domains in two dimensions (2D) and three dimensions  (3D). The irregular domain is embedded in a uniform Cartesian  mesh, but grid points outside of the domain are not used. Second- order local truncation error and the sufficient Gerschgorin criterion  for stability impose some conditions to be satisfied by the weights  of the discretization scheme at a particular interior grid point. A  necessary and sufficient condition, in terms of the anisotropy  matrix, for the existence of a Gerschgorin second-order scheme at  a given interior grid point is found. This theorem is proved in 2D  and 3D. The governing partial differential equations are discretized  through a new technique which uses a linear programming approach  to find the scheme at points far away from the irregular boundary.  Near the irregular boundary, with the addition of boundary  information, special discretizations are found by using an  optimization approach.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783838322339\"\u003e\u003ch3\u003eon Irregular Domains in Two and Three Dimensions\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783838322339","offer_id":39469232193629,"sku":"9783838322339","price":59.0,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/fe22dd56-8bd7-4e27-a4b2-fb47a6e72971.jpg?v=1757744554","url":"https:\/\/shop.autorenwelt.de\/products\/a-numerical-method-for-anisotropic-elliptic-boundary-value-problems-von-miguel-dumett","provider":"Autorenwelt Shop","version":"1.0","type":"link"}