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Progress in adjoint error correction for integral functionals. (English) Zbl 1061.65091

Summary: When approximating the solutions of partial differential equations (PDEs), it is a few key output integrals which are often of most concern. This paper shows how the accuracy of these values can be improved through a correction term which is an inner product of the residual error in the original PDE and the solution of an appropriately defined adjoint PDE. A number of applications is presented and the challenges of smooth reconstruction on unstructured grids and error correction for shocks are discussed.

MSC:

65M25 Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35Q53 KdV equations (Korteweg-de Vries equations)
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs

Software:

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Full Text: DOI

References:

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