Analysis of error bounds of elliptic partial differential equations by using residual correction method

This paper seeks to use the proposed residual correction method in coordination with B-spline functions to obtain upper and lower approximate solutions of elliptic partial differential equations and to further conduct error bounds of mean approximate solution. First, the monotonicity of differential equations is determined, and then the B-spline functions are used to discretize and convert the residual expressions of differential equations into the non-linear mathematical programming problems of inequities. Finally, based on the residual correction concept, the complex constraint solution problems are transformed into simpler iteration problems of equalities.