4 problems

Conjectured regular–singular decomposition. The regular part $u_R$ should admit the above decomposition into a non-oscillating $H^2$ component, an oscillating analytic component, a…

The paper studies finite element discretizations of natural convection problems with sidewall heating, including velocity, pressure, and temperature approximations, and establishes…

Exponential convergence conjecture. The exponential-convergence theorem should also hold when the local degrees of accuracy are chosen according to the graded rule $p_K=j+1$.

Let $X_n$ and $M_n$ be finite element spaces consisting of piecewise polynomials of degrees $p_{X_n}$ and $p_{M_n}$, respectively, with discrete inf-sup constants $\beta_n$ and exa…