6 problems

Let $u$ be the exact solution and $u_h$ the numerical solution produced by the conservative flux optimization finite element scheme, with $\beta$, $\tau_D$, and $\boldsymbol{n}_e$…

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…

Grading of BiSec-MT. There exists a mesh size function $h\in L^1(\Omega)$ with grading $\gamma_h=2$ such that the constants in the equidistribution estimate depend only on…

Consider the hypersingular integral equation on a plane open surface $Gamma$, the model problem in the source, with mesh size $h$ and $N$ denoting the number of unknowns. The appro…

Let the boundary element problem have reduced regularity caused by standard geometric singularities, and consider Crouzeix–Raviart boundary elements on either quasi-uniform or non-…

In topology optimization, let the design found using an adaptively refined mesh be compared with the solution obtained on a uniform fine mesh, and let compliance measure the object…