1,721,005 research outputs found
Stable discretizations of convection-diffusion problems via computable negative-order inner products,
No full textSIAM J. NUMER ANAL
A Fat boundary-type method for localized nonhomogeneous material problems
No full textProblems with localized nonhomogeneous material properties arise frequently in many applications and are a well-known source of difficulty in numerical simulations. In certain applications (including additive manufacturing), the physics of the problem may be considerably more complicated in relatively small portions of the domain, requiring a significantly finer local mesh compared to elsewhere in the domain. This can make the use of a conforming, highly non-uniform mesh numerically unfeasible. In fact, such meshes may be challenging to generate (particularly for regions with complex boundaries) and more difficult to precondition. The problem becomes even more prohibitive when the region requiring a finer-level mesh changes in time, requiring the introduction of refinement and derefinement techniques. To address the aforementioned challenges, we employ a technique related to the Fat boundary method as a possible alternative. We analyze the proposed methodology from a mathematical point of view and validate our findings with a series of two-dimensional numerical tests
The virtual element method for a minimal surface problem
Full text linkIn this paper we consider the Virtual Element discretization of a minimal surface problem, a quasi-linear elliptic partial differential equation modeling the problem of minimizing the area of a surface subject to a prescribed boundary condition. We derive an optimal error estimate and present several numerical tests assessing the validity of the theoretical results
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