4 papers
Hodge Decomposition and Potentials in Variable Exponent Lebesgue and Sobolev Spaces
Anna Balci, Swarnendu Sil, Mikhail Surnachev
The objective of this work is to establish a systematic study of boundary value problems within the framework of differential forms and variable exponent spaces. Specifically, we i…
On the stability of finite-volume schemes on non-uniform meshes
Pavel Bakhvalov, Mikhail Surnachev
In this paper, we study the L2 stability of high-order finite-volume schemes for the 1D transport equation on non-uniform meshes. We consider the case when a small periodic perturb…
On the order of accuracy of finite-volume schemes on unstructured meshes
Pavel Bakhvalov, Mikhail Surnachev
We consider finite-volume schemes for linear hyperbolic systems with constant coefficients on unstructured meshes. Under the stability assumption, they exhibit the convergence rate…
The Lavrentiev phenomenon in calculus of variations with differential forms
Anna Kh. Balci, Mikhail Surnachev
In this article we study convex non-autonomous variational problems with differential forms and corresponding function spaces. We introduce a general framework for constructing cou…