Data-Driven Topology Allocation in Hybrid Finite Element Discretization of Singular Thermoelastic Problems

Abstract

Finite element accuracy for singular problems depends on both mesh resolution and the spatial distribution of approximation capacity. A fixed-budget topology-allocation strategy is developed for hybrid T3–Q4 discretization of a thermoelastic problem on an L-shaped domain with a re-entrant corner. The strategy addresses the allocation problem that arises when the number of Q4 elements is prescribed: rather than increasing the total discretization size, the available Q4 enrichment is spatially redistributed according to its expected contribution to local approximation accuracy. A cell-wise enrichment response derived from paired T3 and Q4 solutions is learned using a Random Forest surrogate with geometric and thermoelastic descriptors. The predicted response is then used to rank cells and construct hybrid topologies at prescribed Q4 budgets. Training uses coarser meshes, while evaluation is performed on held-out resolutions. With 2610 Q4 cells at h = 0.015625, the learned allocation reduces the displacement L2 and elastic-energy errors by 57.6% and 13.7%, respectively, relative to the reference allocation. At h = 0.03125, the corresponding reductions are 47.1% and 7.5%. The results indicate that redistributing a fixed Q4 budget can reduce discretization error across the tested mesh resolutions.