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We develop the analysis of stabilized sparse tensor-product
finite element methods for high-dimensional,
non-self-adjoint and possibly degenerate second-order partial
differential equations of the form
, ,
where is a symmetric positive semidefinite matrix,
using piecewise polynomials of
degree ≥ 1. Our convergence analysis is based on new
high-dimensional approximation results in sparse tensor-product
spaces. We show that the error between the analytical solution and its stabilized
sparse...
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