A Goal-Oriented Adaptive Finite Element Method with Convergence Rates

A Goal-Oriented Adaptive Finite Element Method with Convergence Rates

An adaptive finite element method is analyzed for approximating functionals of the solution of symmetric elliptic second order boundary value problems. We show that the method converges and derive a favorable upper bound for its convergence rate and computational complexity. We illustrate our theoretical findings with numerical results.

Adaptive Finite Element Methods with convergence rates

Convergence of goal-oriented adaptive finite element methods for semilinear problems

In this article we develop convergence theory for a class of goal-oriented adaptive finite element algorithms for second order semilinear elliptic equations. We first introduce several approximate dual problems, and briefly discuss the target problem class. We then review some standard facts concerning conforming finite element discretization and error-estimate-driven adaptive finite element me...

Convergence of Goal-oriented Adaptive Finite Element Methods for Nonsymmetric Problems

In this article we develop convergence theory for a class of goal-oriented adaptive finite element algorithms for second order nonsymmetric linear elliptic equations. In particular, we establish contraction and quasi-optimality results for a method of this type for second order Dirichlet problems involving the elliptic operator Lu = ∇ · (A∇u)− b · ∇u− cu, with A Lipschitz, almost-everywhere sym...

A parallel goal-oriented adaptive finite element method for 2.5D electromagnetic modeling

SUMMARY We present a parallel goal-oriented adaptive finite element method that can be used to rapidly compute highly accurate solutions for 2.5D controlled-source electromagnetic (CSEM) and 2D magnetotelluric (MT) modeling problems. We employ unstructured triangular grids that permit efficient discretization of complex modeling domains such as those containing topography, dipping layers and mu...