SEPARATION PROBLEM FOR STURM-LIOUVILLE EQUATION WITH OPERATOR COEFFICIENT
Let H be a separable Hilbert Space. Denote by H1 = L2(a,b; H) the set of function defned on the interval a < c < b (¾¥ a < c < b £¥) whose values belong to H strongly measurable [12] and satisfying the condition If the inner product of function ¦(c) and g(c) belonging to H1 is defined by then H1 forms a separable Hilbert space. We study separation problem for the operator formed by ¾ y"+ Q (c) y Sturm-Liouville differential expression in L2(¾ ¥, ¥; H) space has been proved where Q (c) in an operator which transforms at H in value of c,,self-adjoint, lower bounded and its inverse is complete continous
Complex geometric features in models would cause generation of redundant elements in finite element analysis.To reduce computation cost of complex models in the premise of acquirement of reliable analysis result,a method for assessing solution space discrepancy between the models before and after simplification is researched.Subdivisions and field functions of the models before and after simplification are compared respectively.Then,degree of such discrepancy can be estimated according to two classic interpolation error theorems for affinity-equivalent conforming elements and isoperimetric elements respectively.The method provides judgment to effectiveness of the simplification strategy.Theory deduction and experiments results indicate that the estimated discrepancy degree is consistent with discrepancy between the two corresponding solution spaces.