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On well-posedness of difference schemes for abstract elliptic problems in L p ([0,T];E) spaces. (English) Zbl 1140.65073
Summary: This paper is devoted to the numerical analysis of abstract elliptic differential equations in L p ([0,T];E) spaces. The presentation uses general approximation scheme and is based on C 0 -semigroup theory and a functional analysis approach. For the solutions of difference scheme of the second-order accuracy, the almost coercive inequality in L τ n p ([0,T];E n ) spaces with the factor min{ln1 τ n |,1+|lnB n B(E n ) |} is obtained. In the case of UMD space E n , we establish a coercive inequality for the same scheme in L τ n p ([0,T];E n ) under the condition of R-boundedness.
65N06Finite difference methods (BVP of PDE)
65J10Equations with linear operators (numerical methods)
47F05Partial differential operators
35J25Second order elliptic equations, boundary value problems
47C10Operators in * -algebras