## A procedure for a posteriori error estimation for $$h$$-$$p$$ finite element methods.(English)Zbl 0778.73060

A new approach to a posteriori error estimation is outlined which is applicable to general $$h-p$$ finite element approximations of general classes of boundary value problems. The approach makes use of duality arguments and is based on the element residual method (ERM). Important aspects of the method are that it provides a systematic approach toward deriving element boundary conditions for the ERM; it leads to an upper bound for the global error in an appropriate energy norm; and it is valid for nonuniform and irregular $$h-p$$ meshes. The approach is applicable to general linear elliptic systems, including unsymmetrical operators, and the method is valid for broad classes of linear and nonlinear problems.

### MSC:

 74S05 Finite element methods applied to problems in solid mechanics 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs
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### References:

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