Goal-oriented A Posteriori Error Estimation for Finite Volume Methods
This work provides a unified error estimation framework for finite volume methods, addressing a known bottleneck in goal-oriented adaptivity for this class of numerical methods.
The paper presents a general framework for goal-oriented a posteriori error estimation for finite volume methods that works directly from the discretized equations, applicable to arbitrary finite volume methods. Numerical results demonstrate the validity and effectiveness of the error estimates for adaptive mesh refinement.
A general framework for goal-oriented a posteriori error estimation for finite volume methods is presented. The framework does not rely on recasting finite volume methods as special cases of finite element methods, but instead directly determines error estimators from the discretized finite volume equations. Thus, the framework can be ap- plied to arbitrary finite volume methods. It also provides the proper functional settings to address well-posedness issues for the primal and adjoint problems. Numerical results are presented to illustrate the validity and effectiveness of the a posteriori error estimates and their applicability to adaptive mesh refinement.