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We present a new class of self-adaptive higher-order finite element methods (-FEM) which are free of analytical
error estimates and thus work equally well for virtually all PDE problems ranging from simple linear elliptic equations to complex time-dependent nonlinear multiphysics coupled problems. The methods do not contain any tuning parameters and work reliably with both
low- and high-order finite elements. The methodology was used to solve various types of problems including thermoelasticity,...
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