diff --git a/dune/tectonic/myblockproblem.hh b/dune/tectonic/myblockproblem.hh
index 352fdb0c5c1a2ecf9ffe8934f2a19f4c119b3b77..e3fae3fffc6783eee4eaf1e260c6749c4850a8ba 100644
--- a/dune/tectonic/myblockproblem.hh
+++ b/dune/tectonic/myblockproblem.hh
@@ -132,7 +132,7 @@ template <class MyConvexProblemTypeTEMPLATE> class MyBlockProblem {
     psi.subDiff(0, D);
     if (D[1] > 0) {
       // NOTE: Numerical instability can actually get us here
-      assert(abs(D[1]) < 1e-15);
+      assert(std::abs(D[1]) < 1e-15);
       return 0;
     }
 
diff --git a/src/one-body-sample.cc b/src/one-body-sample.cc
index e6caf46a20fb1bb5b8e80b61a58295d95b831f25..c5b4f74880df64ff8d3fc00895197337d5b73479 100644
--- a/src/one-body-sample.cc
+++ b/src/one-body-sample.cc
@@ -476,13 +476,15 @@ int main(int argc, char *argv[]) {
 
               double ret1 =
                   compute_state_update_bisection(h, unorm, L, s4_old[i][0]);
-              assert(abs(1.0 / h * ret1 - (s4_old[i] - unorm / L) / h -
-                         exp(-ret1)) < 1e-12);
+              assert(std::abs(1.0 / h * ret1 - (s4_old[i] - unorm / L) / h -
+                              exp(-ret1)) < 1e-11);
+
               double ret2 =
                   compute_state_update_lambert(h, unorm, L, s4_old[i][0]);
-              assert(abs(1.0 / h * ret2 - (s4_old[i] - unorm / L) / h -
-                         exp(-ret2)) < 1e-12);
-              assert(abs(ret2 - ret1) < 1e-14);
+              assert(std::abs(1.0 / h * ret2 - (s4_old[i] - unorm / L) / h -
+                              exp(-ret2)) < 1e-11);
+
+              assert(std::abs(ret2 - ret1) < 1e-14);
 
               (*s4_new)[i][0] = ret1;
             }
@@ -540,13 +542,13 @@ int main(int argc, char *argv[]) {
 
               double ret1 =
                   compute_state_update_bisection(h, unorm, L, s5_old[i][0]);
-              assert(abs(1.0 / h * ret1 - (s5_old[i] - unorm / L) / h -
-                         exp(-ret1)) < 1e-12);
+              assert(std::abs(1.0 / h * ret1 - (s5_old[i] - unorm / L) / h -
+                              exp(-ret1)) < 1e-12);
               double ret2 =
                   compute_state_update_lambert(h, unorm, L, s5_old[i][0]);
-              assert(abs(1.0 / h * ret2 - (s5_old[i] - unorm / L) / h -
-                         exp(-ret2)) < 1e-12);
-              assert(abs(ret2 - ret1) < 1e-14);
+              assert(std::abs(1.0 / h * ret2 - (s5_old[i] - unorm / L) / h -
+                              exp(-ret2)) < 1e-12);
+              assert(std::abs(ret2 - ret1) < 1e-14);
 
               (*s5_new)[i][0] = ret1;
             }