A unified framework is introduced for finite element and box discretizations of fractional powers of elliptic operators, where mass lumping produces the intrinsic fractional box method and error estimates are derived under consistency assumptions.
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Existence of optimal solutions together with first-order and necessary/sufficient second-order optimality conditions are established for pointwise tracking optimal control of a fractional semilinear elliptic PDE.
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Finite element and box-method discretizations for fractional elliptic problems with quadrature and mass lumping
A unified framework is introduced for finite element and box discretizations of fractional powers of elliptic operators, where mass lumping produces the intrinsic fractional box method and error estimates are derived under consistency assumptions.