We study theoretical and practical issues arising in the implementation of the Finite Element
Method for a strongly elliptic second order equation with jump discontinuities in its …

We construct a symmetric interior penalty method for an elliptic distributed optimal control
problem with pointwise state constraints on general polygonal domains. The resulting …

We consider an elliptic distributed optimal control problem on convex polygonal domains
with pointwise state constraints and solve it as a fourth order variational inequality for the …

$C^0$ Interior Penalty Methods for an Elliptic Distributed Optimal Control Problem on
Nonconvex Polygonal Domains with Pointwise Page 1 Copyright © by SIAM. Unauthorized …

Let [Formula: see text] be the distance function to the origin O∈ R2, and let us fix δ> 0. We
consider the “Schrödinger-type mixed boundary value problem”− Δu+ δr− 2u= f∈ Hm− 1 (Ω) …

It is well known that the regularity of solutions of elliptic partial differential equations on
domains with re-entrant corners is limited by the maximal interior angle. This results in …

We study a class of symmetric discontinuous Galerkin methods on graded meshes. Optimal
order error estimates are derived in both the energy norm and the L 2 norm, and we …

The symmetric interior penalty (SIP) method on graded meshes and its fast solution by
multigrid methods are studied in this paper. We obtain quasi‐optimal error estimates in both …

P1 finite element methods for an elliptic optimal control problem with pointwise state
constraints Page 1 IMA Journal of Numerical Analysis (2020) 40, 1–28 doi:10.1093/imanum/dry071 …

Abstract Let L≔− r− 2 (r∂ r) 2−∂ z 2. We consider the equation L u= f on a bounded
polygonal domain with suitable boundary conditions, derived from the three-dimensional …