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Interior regularity estimates for elliptic systems of difference equations. (English) Zbl 0561.65070

We prove interior regularity estimates for a large class of difference approximations for elliptic systems of partial differential equations. These estimates are analogous to those for the systems of differential equations. From these regularity estimates we obtain estimates on the convergence of the solutions of the difference equations. A theory of pseudo-difference operators with order is used to prove the regularity results. We also comment on factors to be considered in choosing a difference scheme for computations.

MSC:

65N06 Finite difference methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
39A70 Difference operators
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