High Order Compact Finite Volume Scheme For Interface Problem With Two Mixed Point Boundary Conditions

This thesis mainly studies a class of two mixed point boundary value with the interface problem. By using the node transfer technology, a compact finite volume element method is proposed to solve this problem. First of all, according to the inter-face problem of the two mixed boundary value it proposes a compact finite volume element format. The linear algebraic system derived by this scheme has better tridiag-onal property, and can be solved by Thomas method. Secondly, using the theoretical analysis it proves that the scheme is convergent with fourth-order accuracy in the H1 discrete semi norm. Using functional value at node, the post-processing formulas for the functional value and first derivative value at midpoint of every element are obtained, which both also have fourth order accuracy. Finally, through numerical ex-periment, it verifies the correctness of the theoretical analysis and the effectiveness of the proposed scheme.